diff --git a/src/transformation/utils/diagnostics.ts b/src/transformation/utils/diagnostics.ts
index 94f7781de..fd443e596 100644
--- a/src/transformation/utils/diagnostics.ts
+++ b/src/transformation/utils/diagnostics.ts
@@ -155,3 +155,11 @@ export const unsupportedOptionalCompileMembersOnly = createErrorDiagnosticFactor
 export const undefinedInArrayLiteral = createErrorDiagnosticFactory(
     "Array literals may not contain undefined or null."
 );
+
+export const invalidMethodCallExtensionUse = createErrorDiagnosticFactory(
+    "This language extension must be called as a method."
+);
+
+export const invalidSpreadInCallExtension = createErrorDiagnosticFactory(
+    "Spread elements are not supported in call extensions."
+);
diff --git a/src/transformation/utils/language-extensions.ts b/src/transformation/utils/language-extensions.ts
index 881da105b..108c6eef1 100644
--- a/src/transformation/utils/language-extensions.ts
+++ b/src/transformation/utils/language-extensions.ts
@@ -1,5 +1,6 @@
 import * as ts from "typescript";
 import { TransformationContext } from "../context";
+import { invalidMethodCallExtensionUse, invalidSpreadInCallExtension } from "./diagnostics";
 
 export enum ExtensionKind {
     MultiFunction = "MultiFunction",
@@ -53,6 +54,7 @@ export enum ExtensionKind {
     TableAddKeyType = "TableAddKey",
     TableAddKeyMethodType = "TableAddKeyMethod",
 }
+
 const extensionValues: Set<string> = new Set(Object.values(ExtensionKind));
 
 export function getExtensionKindForType(context: TransformationContext, type: ts.Type): ExtensionKind | undefined {
@@ -119,3 +121,78 @@ export function getIterableExtensionKindForNode(
     const type = context.checker.getTypeAtLocation(node);
     return getIterableExtensionTypeForType(context, type);
 }
+
+export const methodExtensionKinds: ReadonlySet<ExtensionKind> = new Set<ExtensionKind>([
+    ExtensionKind.AdditionOperatorMethodType,
+    ExtensionKind.SubtractionOperatorMethodType,
+    ExtensionKind.MultiplicationOperatorMethodType,
+    ExtensionKind.DivisionOperatorMethodType,
+    ExtensionKind.ModuloOperatorMethodType,
+    ExtensionKind.PowerOperatorMethodType,
+    ExtensionKind.FloorDivisionOperatorMethodType,
+    ExtensionKind.BitwiseAndOperatorMethodType,
+    ExtensionKind.BitwiseOrOperatorMethodType,
+    ExtensionKind.BitwiseExclusiveOrOperatorMethodType,
+    ExtensionKind.BitwiseLeftShiftOperatorMethodType,
+    ExtensionKind.BitwiseRightShiftOperatorMethodType,
+    ExtensionKind.ConcatOperatorMethodType,
+    ExtensionKind.LessThanOperatorMethodType,
+    ExtensionKind.GreaterThanOperatorMethodType,
+    ExtensionKind.NegationOperatorMethodType,
+    ExtensionKind.BitwiseNotOperatorMethodType,
+    ExtensionKind.LengthOperatorMethodType,
+    ExtensionKind.TableDeleteMethodType,
+    ExtensionKind.TableGetMethodType,
+    ExtensionKind.TableHasMethodType,
+    ExtensionKind.TableSetMethodType,
+    ExtensionKind.TableAddKeyMethodType,
+]);
+
+export function getNaryCallExtensionArgs(
+    context: TransformationContext,
+    node: ts.CallExpression,
+    kind: ExtensionKind,
+    numArgs: number
+): readonly ts.Expression[] | undefined {
+    let expressions: readonly ts.Expression[];
+    if (node.arguments.some(ts.isSpreadElement)) {
+        context.diagnostics.push(invalidSpreadInCallExtension(node));
+        return undefined;
+    }
+    if (methodExtensionKinds.has(kind)) {
+        if (!(ts.isPropertyAccessExpression(node.expression) || ts.isElementAccessExpression(node.expression))) {
+            context.diagnostics.push(invalidMethodCallExtensionUse(node));
+            return undefined;
+        }
+        if (node.arguments.length < numArgs - 1) {
+            // assumed to be TS error
+            return undefined;
+        }
+        expressions = [node.expression.expression, ...node.arguments];
+    } else {
+        if (node.arguments.length < numArgs) {
+            // assumed to be TS error
+            return undefined;
+        }
+        expressions = node.arguments;
+    }
+    return expressions;
+}
+
+export function getUnaryCallExtensionArg(
+    context: TransformationContext,
+    node: ts.CallExpression,
+    kind: ExtensionKind
+): ts.Expression | undefined {
+    return getNaryCallExtensionArgs(context, node, kind, 1)?.[0];
+}
+
+export function getBinaryCallExtensionArgs(
+    context: TransformationContext,
+    node: ts.CallExpression,
+    kind: ExtensionKind
+): readonly [ts.Expression, ts.Expression] | undefined {
+    const expressions = getNaryCallExtensionArgs(context, node, kind, 2);
+    if (expressions === undefined) return undefined;
+    return [expressions[0], expressions[1]];
+}
diff --git a/src/transformation/visitors/language-extensions/operators.ts b/src/transformation/visitors/language-extensions/operators.ts
index 657c98b92..4cb08abc2 100644
--- a/src/transformation/visitors/language-extensions/operators.ts
+++ b/src/transformation/visitors/language-extensions/operators.ts
@@ -4,8 +4,9 @@ import { TransformationContext } from "../../context";
 import { assert } from "../../../utils";
 import { LuaTarget } from "../../../CompilerOptions";
 import { unsupportedForTarget } from "../../utils/diagnostics";
-import { ExtensionKind } from "../../utils/language-extensions";
+import { ExtensionKind, getBinaryCallExtensionArgs, getUnaryCallExtensionArg } from "../../utils/language-extensions";
 import { LanguageExtensionCallTransformerMap } from "./call-extension";
+import { transformOrderedExpressions } from "../expression-list";
 
 const binaryOperatorMappings = new Map<ExtensionKind, lua.BinaryOperator>([
     [ExtensionKind.AdditionOperatorType, lua.SyntaxKind.AdditionOperator],
@@ -81,35 +82,21 @@ for (const kind of unaryOperatorMappings.keys()) {
 function transformBinaryOperator(context: TransformationContext, node: ts.CallExpression, kind: ExtensionKind) {
     if (requiresLua53.has(kind)) checkHasLua53(context, node, kind);
 
-    let args: readonly ts.Expression[] = node.arguments;
-    if (
-        args.length === 1 &&
-        (ts.isPropertyAccessExpression(node.expression) || ts.isElementAccessExpression(node.expression))
-    ) {
-        args = [node.expression.expression, ...args];
-    }
+    const args = getBinaryCallExtensionArgs(context, node, kind);
+    if (!args) return lua.createNilLiteral();
+
+    const [left, right] = transformOrderedExpressions(context, args);
 
     const luaOperator = binaryOperatorMappings.get(kind);
     assert(luaOperator);
-    return lua.createBinaryExpression(
-        context.transformExpression(args[0]),
-        context.transformExpression(args[1]),
-        luaOperator
-    );
+    return lua.createBinaryExpression(left, right, luaOperator);
 }
 
 function transformUnaryOperator(context: TransformationContext, node: ts.CallExpression, kind: ExtensionKind) {
     if (requiresLua53.has(kind)) checkHasLua53(context, node, kind);
 
-    let arg: ts.Expression;
-    if (
-        node.arguments.length === 0 &&
-        (ts.isPropertyAccessExpression(node.expression) || ts.isElementAccessExpression(node.expression))
-    ) {
-        arg = node.expression.expression;
-    } else {
-        arg = node.arguments[0];
-    }
+    const arg = getUnaryCallExtensionArg(context, node, kind);
+    if (!arg) return lua.createNilLiteral();
 
     const luaOperator = unaryOperatorMappings.get(kind);
     assert(luaOperator);
diff --git a/src/transformation/visitors/language-extensions/table.ts b/src/transformation/visitors/language-extensions/table.ts
index 2d22adf15..d3aaedc5d 100644
--- a/src/transformation/visitors/language-extensions/table.ts
+++ b/src/transformation/visitors/language-extensions/table.ts
@@ -1,16 +1,22 @@
 import * as ts from "typescript";
 import * as lua from "../../../LuaAST";
 import { TransformationContext } from "../../context";
-import { ExtensionKind, getExtensionKindForNode } from "../../utils/language-extensions";
-import { transformExpressionList } from "../expression-list";
-import { LanguageExtensionCallTransformer } from "./call-extension";
+import {
+    ExtensionKind,
+    getBinaryCallExtensionArgs,
+    getExtensionKindForNode,
+    getNaryCallExtensionArgs,
+} from "../../utils/language-extensions";
+import { transformOrderedExpressions } from "../expression-list";
+import { LanguageExtensionCallTransformerMap } from "./call-extension";
 
 export function isTableNewCall(context: TransformationContext, node: ts.NewExpression) {
     return getExtensionKindForNode(context, node.expression) === ExtensionKind.TableNewType;
 }
+
 export const tableNewExtensions = [ExtensionKind.TableNewType];
 
-export const tableExtensionTransformers: { [P in ExtensionKind]?: LanguageExtensionCallTransformer } = {
+export const tableExtensionTransformers: LanguageExtensionCallTransformerMap = {
     [ExtensionKind.TableDeleteType]: transformTableDeleteExpression,
     [ExtensionKind.TableDeleteMethodType]: transformTableDeleteExpression,
     [ExtensionKind.TableGetType]: transformTableGetExpression,
@@ -19,8 +25,8 @@ export const tableExtensionTransformers: { [P in ExtensionKind]?: LanguageExtens
     [ExtensionKind.TableHasMethodType]: transformTableHasExpression,
     [ExtensionKind.TableSetType]: transformTableSetExpression,
     [ExtensionKind.TableSetMethodType]: transformTableSetExpression,
-    [ExtensionKind.TableAddKeyType]: transformTableAddExpression,
-    [ExtensionKind.TableAddKeyMethodType]: transformTableAddExpression,
+    [ExtensionKind.TableAddKeyType]: transformTableAddKeyExpression,
+    [ExtensionKind.TableAddKeyMethodType]: transformTableAddKeyExpression,
 };
 
 function transformTableDeleteExpression(
@@ -28,48 +34,32 @@ function transformTableDeleteExpression(
     node: ts.CallExpression,
     extensionKind: ExtensionKind
 ): lua.Expression {
-    const args = node.arguments.slice();
-    if (
-        extensionKind === ExtensionKind.TableDeleteMethodType &&
-        (ts.isPropertyAccessExpression(node.expression) || ts.isElementAccessExpression(node.expression))
-    ) {
-        // In case of method (no table argument), push method owner to front of args list
-        args.unshift(node.expression.expression);
+    const args = getBinaryCallExtensionArgs(context, node, extensionKind);
+    if (!args) {
+        return lua.createNilLiteral();
     }
 
-    const [table, accessExpression] = transformExpressionList(context, args);
+    const [table, key] = transformOrderedExpressions(context, args);
     // arg0[arg1] = nil
     context.addPrecedingStatements(
-        lua.createAssignmentStatement(
-            lua.createTableIndexExpression(table, accessExpression),
-            lua.createNilLiteral(),
-            node
-        )
+        lua.createAssignmentStatement(lua.createTableIndexExpression(table, key), lua.createNilLiteral(), node)
     );
     return lua.createBooleanLiteral(true);
 }
 
-function transformWithTableArgument(context: TransformationContext, node: ts.CallExpression): lua.Expression[] {
-    if (ts.isPropertyAccessExpression(node.expression) || ts.isElementAccessExpression(node.expression)) {
-        return transformExpressionList(context, [node.expression.expression, ...node.arguments]);
-    }
-    // todo: report diagnostic?
-    return [lua.createNilLiteral(), ...transformExpressionList(context, node.arguments)];
-}
-
 function transformTableGetExpression(
     context: TransformationContext,
     node: ts.CallExpression,
     extensionKind: ExtensionKind
 ): lua.Expression {
-    const args =
-        extensionKind === ExtensionKind.TableGetMethodType
-            ? transformWithTableArgument(context, node)
-            : transformExpressionList(context, node.arguments);
+    const args = getBinaryCallExtensionArgs(context, node, extensionKind);
+    if (!args) {
+        return lua.createNilLiteral();
+    }
 
-    const [table, accessExpression] = args;
+    const [table, key] = transformOrderedExpressions(context, args);
     // arg0[arg1]
-    return lua.createTableIndexExpression(table, accessExpression, node);
+    return lua.createTableIndexExpression(table, key, node);
 }
 
 function transformTableHasExpression(
@@ -77,14 +67,14 @@ function transformTableHasExpression(
     node: ts.CallExpression,
     extensionKind: ExtensionKind
 ): lua.Expression {
-    const args =
-        extensionKind === ExtensionKind.TableHasMethodType
-            ? transformWithTableArgument(context, node)
-            : transformExpressionList(context, node.arguments);
+    const args = getBinaryCallExtensionArgs(context, node, extensionKind);
+    if (!args) {
+        return lua.createNilLiteral();
+    }
 
-    const [table, accessExpression] = args;
+    const [table, key] = transformOrderedExpressions(context, args);
     // arg0[arg1]
-    const tableIndexExpression = lua.createTableIndexExpression(table, accessExpression);
+    const tableIndexExpression = lua.createTableIndexExpression(table, key);
 
     // arg0[arg1] ~= nil
     return lua.createBinaryExpression(
@@ -100,37 +90,33 @@ function transformTableSetExpression(
     node: ts.CallExpression,
     extensionKind: ExtensionKind
 ): lua.Expression {
-    const args =
-        extensionKind === ExtensionKind.TableSetMethodType
-            ? transformWithTableArgument(context, node)
-            : transformExpressionList(context, node.arguments);
+    const args = getNaryCallExtensionArgs(context, node, extensionKind, 3);
+    if (!args) {
+        return lua.createNilLiteral();
+    }
 
-    const [table, accessExpression, value] = args;
+    const [table, key, value] = transformOrderedExpressions(context, args);
     // arg0[arg1] = arg2
     context.addPrecedingStatements(
-        lua.createAssignmentStatement(lua.createTableIndexExpression(table, accessExpression), value, node)
+        lua.createAssignmentStatement(lua.createTableIndexExpression(table, key), value, node)
     );
     return lua.createNilLiteral();
 }
 
-function transformTableAddExpression(
+function transformTableAddKeyExpression(
     context: TransformationContext,
     node: ts.CallExpression,
     extensionKind: ExtensionKind
 ): lua.Expression {
-    const args =
-        extensionKind === ExtensionKind.TableAddKeyMethodType
-            ? transformWithTableArgument(context, node)
-            : transformExpressionList(context, node.arguments);
+    const args = getNaryCallExtensionArgs(context, node, extensionKind, 2);
+    if (!args) {
+        return lua.createNilLiteral();
+    }
 
-    const [table, value] = args;
+    const [table, key] = transformOrderedExpressions(context, args);
     // arg0[arg1] = true
     context.addPrecedingStatements(
-        lua.createAssignmentStatement(
-            lua.createTableIndexExpression(table, value),
-            lua.createBooleanLiteral(true),
-            node
-        )
+        lua.createAssignmentStatement(lua.createTableIndexExpression(table, key), lua.createBooleanLiteral(true), node)
     );
     return lua.createNilLiteral();
 }
diff --git a/test/unit/__snapshots__/optionalChaining.spec.ts.snap b/test/unit/__snapshots__/optionalChaining.spec.ts.snap
index e52fe69b8..707ecf68b 100644
--- a/test/unit/__snapshots__/optionalChaining.spec.ts.snap
+++ b/test/unit/__snapshots__/optionalChaining.spec.ts.snap
@@ -63,11 +63,13 @@ exports[`Unsupported optional chains Compile members only: diagnostics 1`] = `"m
 exports[`Unsupported optional chains Language extensions: code 1`] = `
 "local ____opt_0 = ({}).has
 if ____opt_0 ~= nil then
-    local ____ = nil[3] ~= nil
 end"
 `;
 
-exports[`Unsupported optional chains Language extensions: diagnostics 1`] = `"main.ts(2,17): error TSTL: Optional calls are not supported for builtin or language extension functions."`;
+exports[`Unsupported optional chains Language extensions: diagnostics 1`] = `
+"main.ts(2,17): error TSTL: Optional calls are not supported for builtin or language extension functions.
+main.ts(2,17): error TSTL: This language extension must be called as a method."
+`;
 
 exports[`long optional chain 1`] = `
 "local ____exports = {}
diff --git a/test/unit/language-extensions/__snapshots__/operators.spec.ts.snap b/test/unit/language-extensions/__snapshots__/operators.spec.ts.snap
index dda0e61e2..a4554a8a1 100644
--- a/test/unit/language-extensions/__snapshots__/operators.spec.ts.snap
+++ b/test/unit/language-extensions/__snapshots__/operators.spec.ts.snap
@@ -1,5 +1,17 @@
 // Jest Snapshot v1, https://goo.gl/fbAQLP
 
+exports[`does not crash on invalid operator use global function: code 1`] = `""`;
+
+exports[`does not crash on invalid operator use global function: diagnostics 1`] = `"main.ts(3,13): error TS2554: Expected 2 arguments, but got 1."`;
+
+exports[`does not crash on invalid operator use method: code 1`] = `"left = {}"`;
+
+exports[`does not crash on invalid operator use method: diagnostics 1`] = `"main.ts(5,18): error TS2554: Expected 1 arguments, but got 0."`;
+
+exports[`does not crash on invalid operator use unary operator: code 1`] = `"op(_G)"`;
+
+exports[`does not crash on invalid operator use unary operator: diagnostics 1`] = `"main.ts(2,31): error TS2304: Cannot find name 'LuaUnaryMinus'."`;
+
 exports[`operator mapping - invalid use (const foo = (op as any)(1, 2);): code 1`] = `"foo = op(_G, 1, 2)"`;
 
 exports[`operator mapping - invalid use (const foo = (op as any)(1, 2);): diagnostics 1`] = `"main.ts(3,22): error TSTL: This function must be called directly and cannot be referred to."`;
diff --git a/test/unit/language-extensions/__snapshots__/table.spec.ts.snap b/test/unit/language-extensions/__snapshots__/table.spec.ts.snap
index 9821d9777..5bf4ef2c8 100644
--- a/test/unit/language-extensions/__snapshots__/table.spec.ts.snap
+++ b/test/unit/language-extensions/__snapshots__/table.spec.ts.snap
@@ -133,3 +133,11 @@ __TS__ArrayMap({\\"a\\", \\"b\\", \\"c\\"}, ____table.has)"
 `;
 
 exports[`LuaTableHas extension invalid use method expression ("LuaTable<string, number>"): diagnostics 1`] = `"main.ts(3,37): error TSTL: This function must be called directly and cannot be referred to."`;
+
+exports[`does not crash on invalid extension use global function: code 1`] = `""`;
+
+exports[`does not crash on invalid extension use global function: diagnostics 1`] = `"main.ts(3,9): error TS2554: Expected 2 arguments, but got 1."`;
+
+exports[`does not crash on invalid extension use method: code 1`] = `"left = {}"`;
+
+exports[`does not crash on invalid extension use method: diagnostics 1`] = `"main.ts(5,14): error TS2554: Expected 2 arguments, but got 0."`;
diff --git a/test/unit/language-extensions/operators.spec.ts b/test/unit/language-extensions/operators.spec.ts
index 043b1cebb..303a5d0be 100644
--- a/test/unit/language-extensions/operators.spec.ts
+++ b/test/unit/language-extensions/operators.spec.ts
@@ -2,7 +2,11 @@ import * as path from "path";
 import * as util from "../../util";
 import * as tstl from "../../../src";
 import { LuaTarget } from "../../../src";
-import { unsupportedForTarget, invalidCallExtensionUse } from "../../../src/transformation/utils/diagnostics";
+import {
+    unsupportedForTarget,
+    invalidCallExtensionUse,
+    invalidSpreadInCallExtension,
+} from "../../../src/transformation/utils/diagnostics";
 
 const operatorsProjectOptions: tstl.CompilerOptions = {
     luaTarget: LuaTarget.Lua54,
@@ -389,3 +393,41 @@ test.each([
         .setOptions(operatorsProjectOptions)
         .expectDiagnosticsToMatchSnapshot([invalidCallExtensionUse.code]);
 });
+
+describe("does not crash on invalid operator use", () => {
+    test("global function", () => {
+        util.testModule`
+            declare const op: LuaAddition<number, number, number>;
+            op(1)
+    `
+            .setOptions(operatorsProjectOptions)
+            .expectDiagnosticsToMatchSnapshot();
+    });
+    test("unary operator", () => {
+        util.testModule`
+            declare const op: LuaUnaryMinus<number, number>;
+            op()
+    `
+            .setOptions(operatorsProjectOptions)
+            .expectDiagnosticsToMatchSnapshot();
+    });
+    test("method", () => {
+        util.testModule`
+            const left = {} as {
+                op: LuaAdditionMethod<number, number>;
+            }
+            left.op()
+    `
+            .setOptions(operatorsProjectOptions)
+            .expectDiagnosticsToMatchSnapshot();
+    });
+});
+
+test("does not allow spread", () => {
+    util.testModule`
+        declare const op: LuaAddition<number, number, number>;
+        op(...[1, 2] as const);
+    `
+        .setOptions(operatorsProjectOptions)
+        .expectToHaveDiagnostics([invalidSpreadInCallExtension.code]);
+});
diff --git a/test/unit/language-extensions/table.spec.ts b/test/unit/language-extensions/table.spec.ts
index ed9e8e37c..b833de22b 100644
--- a/test/unit/language-extensions/table.spec.ts
+++ b/test/unit/language-extensions/table.spec.ts
@@ -467,3 +467,25 @@ test.each([
         .withLanguageExtensions()
         .expectToEqual(expected);
 });
+
+describe("does not crash on invalid extension use", () => {
+    test("global function", () => {
+        util.testModule`
+        declare const op: LuaTableGet<{}, string, any>
+        op({})
+        `
+            .withLanguageExtensions()
+            .expectDiagnosticsToMatchSnapshot();
+    });
+
+    test("method", () => {
+        util.testModule`
+        const left = {} as {
+            op: LuaTableGet<{}, string, any>
+        }
+        left.op()
+        `
+            .withLanguageExtensions()
+            .expectDiagnosticsToMatchSnapshot();
+    });
+});