diff --git a/packages/babel-plugin-transform-classes/src/transformClass.ts b/packages/babel-plugin-transform-classes/src/transformClass.ts
index fcaaac5445bc..7597b6a556f6 100644
--- a/packages/babel-plugin-transform-classes/src/transformClass.ts
+++ b/packages/babel-plugin-transform-classes/src/transformClass.ts
@@ -62,6 +62,8 @@ export default function transformClass(
     protoAlias: null,
     isLoose: false,
 
+    dynamicKeys: new Map(),
+
     methods: {
       // 'list' is in the same order as the elements appear in the class body.
       // if there aren't computed keys, we can safely reorder class elements
@@ -600,8 +602,26 @@ export default function transformClass(
     );
   }
 
+  function extractDynamicKeys() {
+    const { dynamicKeys, node, scope } = classState as {
+      dynamicKeys: Map<string, t.Expression>;
+      node: t.Class;
+      scope: NodePath["scope"];
+    };
+
+    node.body.body.forEach(elem => {
+      if (!t.isClassMethod(elem) || !elem.computed) return;
+      if (scope.isPure(elem.key, /* constatns only*/ true)) return;
+
+      const id = path.scope.generateUidIdentifierBasedOnNode(elem.key);
+      dynamicKeys.set(id.name, elem.key);
+
+      elem.key = id;
+    });
+  }
+
   function setupClosureParamsArgs() {
-    const { superName } = classState;
+    const { superName, dynamicKeys } = classState;
     const closureParams = [];
     const closureArgs = [];
 
@@ -623,6 +643,11 @@ export default function transformClass(
       setState({ superName: t.cloneNode(param) });
     }
 
+    for (const [name, value] of dynamicKeys) {
+      closureParams.push(t.identifier(name));
+      closureArgs.push(value);
+    }
+
     return { closureParams, closureArgs };
   }
 
@@ -668,6 +693,8 @@ export default function transformClass(
       construct: buildConstructor(classRef, constructorBody, node),
     });
 
+    extractDynamicKeys();
+
     let { body } = classState;
     const { closureParams, closureArgs } = setupClosureParamsArgs();
 
diff --git a/packages/babel-plugin-transform-classes/test/fixtures/get-set/change-computed-key/output.js b/packages/babel-plugin-transform-classes/test/fixtures/get-set/change-computed-key/output.js
index 8e5ae962c606..a08a170daf74 100644
--- a/packages/babel-plugin-transform-classes/test/fixtures/get-set/change-computed-key/output.js
+++ b/packages/babel-plugin-transform-classes/test/fixtures/get-set/change-computed-key/output.js
@@ -1,4 +1,4 @@
-let A = /*#__PURE__*/function () {
+let A = /*#__PURE__*/function (_x, _ref, _x2) {
   "use strict";
 
   function A() {
@@ -6,14 +6,14 @@ let A = /*#__PURE__*/function () {
   }
 
   babelHelpers.createClass(A, [{
-    key: x,
+    key: _x,
     get: function () {}
   }, {
-    key: (x = 2, 3),
+    key: _ref,
     value: function () {}
   }, {
-    key: x,
+    key: _x2,
     set: function (_) {}
   }]);
   return A;
-}();
+}(x, (x = 2, 3), x);
diff --git a/packages/babel-plugin-transform-classes/test/fixtures/spec/computed-key-class-tdz/exec.js b/packages/babel-plugin-transform-classes/test/fixtures/spec/computed-key-class-tdz/exec.js
new file mode 100644
index 000000000000..afb11a7419e7
--- /dev/null
+++ b/packages/babel-plugin-transform-classes/test/fixtures/spec/computed-key-class-tdz/exec.js
@@ -0,0 +1,5 @@
+expect(() => {
+  class A {
+    [A.name]() {}
+  }
+}).toThrow(ReferenceError);
diff --git a/packages/babel-plugin-transform-classes/test/fixtures/spec/computed-key-class-tdz/options.json b/packages/babel-plugin-transform-classes/test/fixtures/spec/computed-key-class-tdz/options.json
new file mode 100644
index 000000000000..2e14e9fc86cb
--- /dev/null
+++ b/packages/babel-plugin-transform-classes/test/fixtures/spec/computed-key-class-tdz/options.json
@@ -0,0 +1,4 @@
+{
+  "plugins": ["transform-classes"],
+  "minNodeVersion": "10.0.0"
+}
diff --git a/packages/babel-plugin-transform-classes/test/fixtures/spec/computed-keys-call-order/exec.js b/packages/babel-plugin-transform-classes/test/fixtures/spec/computed-keys-call-order/exec.js
new file mode 100644
index 000000000000..f1e7372457c8
--- /dev/null
+++ b/packages/babel-plugin-transform-classes/test/fixtures/spec/computed-keys-call-order/exec.js
@@ -0,0 +1,11 @@
+var log = [];
+
+class A {
+  [log.push(1)]() {}
+  static [log.push(2)]() {}
+  [log.push(3)]() {}
+  static [log.push(4)]() {}
+}
+
+expect(log).toEqual([1, 2, 3, 4]);
+
diff --git a/packages/babel-plugin-transform-classes/test/fixtures/spec/computed-keys-yield-await/input.js b/packages/babel-plugin-transform-classes/test/fixtures/spec/computed-keys-yield-await/input.js
new file mode 100644
index 000000000000..c7995163ed03
--- /dev/null
+++ b/packages/babel-plugin-transform-classes/test/fixtures/spec/computed-keys-yield-await/input.js
@@ -0,0 +1,9 @@
+async function* fn() {
+  class A {
+    [yield 1]() {}
+  }
+
+  class B extends A {
+    [await 1]() {}
+  }
+}
diff --git a/packages/babel-plugin-transform-classes/test/fixtures/spec/computed-keys-yield-await/output.js b/packages/babel-plugin-transform-classes/test/fixtures/spec/computed-keys-yield-await/output.js
new file mode 100644
index 000000000000..aec80d976bac
--- /dev/null
+++ b/packages/babel-plugin-transform-classes/test/fixtures/spec/computed-keys-yield-await/output.js
@@ -0,0 +1,34 @@
+async function* fn() {
+  var A = /*#__PURE__*/function (_yield$) {
+    "use strict";
+
+    function A() {
+      babelHelpers.classCallCheck(this, A);
+    }
+
+    babelHelpers.createClass(A, [{
+      key: _yield$,
+      value: function value() {}
+    }]);
+    return A;
+  }(yield 1);
+
+  var B = /*#__PURE__*/function (_A, _await$) {
+    "use strict";
+
+    babelHelpers.inherits(B, _A);
+
+    var _super = babelHelpers.createSuper(B);
+
+    function B() {
+      babelHelpers.classCallCheck(this, B);
+      return _super.apply(this, arguments);
+    }
+
+    babelHelpers.createClass(B, [{
+      key: _await$,
+      value: function value() {}
+    }]);
+    return B;
+  }(A, await 1);
+}
diff --git a/packages/babel-plugin-transform-classes/test/fixtures/spec/computed-methods/output.js b/packages/babel-plugin-transform-classes/test/fixtures/spec/computed-methods/output.js
index ef64056212c7..bc107f1a1b90 100644
--- a/packages/babel-plugin-transform-classes/test/fixtures/spec/computed-methods/output.js
+++ b/packages/babel-plugin-transform-classes/test/fixtures/spec/computed-methods/output.js
@@ -1,4 +1,4 @@
-var Foo = /*#__PURE__*/function () {
+var Foo = /*#__PURE__*/function (_bar, _ref) {
   "use strict";
 
   function Foo() {
@@ -11,11 +11,11 @@ var Foo = /*#__PURE__*/function () {
       "second";
     }
   }, {
-    key: bar,
+    key: _bar,
     value: function value() {}
   }, {
-    key: bar + "foo",
+    key: _ref,
     value: function value() {}
   }]);
   return Foo;
-}();
+}(bar, bar + "foo");
diff --git a/packages/babel-plugin-transform-classes/test/fixtures/spec/name-collisions-with-class-ref-in-computed-key/output.js b/packages/babel-plugin-transform-classes/test/fixtures/spec/name-collisions-with-class-ref-in-computed-key/output.js
index 71b59391fdeb..84bdf2ee075c 100644
--- a/packages/babel-plugin-transform-classes/test/fixtures/spec/name-collisions-with-class-ref-in-computed-key/output.js
+++ b/packages/babel-plugin-transform-classes/test/fixtures/spec/name-collisions-with-class-ref-in-computed-key/output.js
@@ -11,21 +11,21 @@ var Foo = /*#__PURE__*/function (_Bar) {
     babelHelpers.classCallCheck(this, Foo);
     _this = _super.call(this);
 
-    var X = /*#__PURE__*/function () {
+    var X = /*#__PURE__*/function (_ref) {
       function X() {
         babelHelpers.classCallCheck(this, X);
       }
 
       babelHelpers.createClass(X, [{
-        key: (() => {
-          var _Foo;
-
-          babelHelpers.get((_thisSuper = babelHelpers.assertThisInitialized(_this), babelHelpers.getPrototypeOf(Foo.prototype)), "method", _thisSuper).call(_thisSuper);
-        })(),
+        key: _ref,
         value: function value() {}
       }]);
       return X;
-    }();
+    }((() => {
+      var _Foo;
+
+      babelHelpers.get((_thisSuper = babelHelpers.assertThisInitialized(_this), babelHelpers.getPrototypeOf(Foo.prototype)), "method", _thisSuper).call(_thisSuper);
+    })());
 
     return _this;
   }
diff --git a/packages/babel-plugin-transform-classes/test/fixtures/spec/nested-class-super-call-in-key/output.js b/packages/babel-plugin-transform-classes/test/fixtures/spec/nested-class-super-call-in-key/output.js
index fe4902958d94..b1e76457cf36 100644
--- a/packages/babel-plugin-transform-classes/test/fixtures/spec/nested-class-super-call-in-key/output.js
+++ b/packages/babel-plugin-transform-classes/test/fixtures/spec/nested-class-super-call-in-key/output.js
@@ -16,25 +16,23 @@ var Outer = /*#__PURE__*/function (_Hello) {
   var _super = babelHelpers.createSuper(Outer);
 
   function Outer() {
-    var _this2 = this;
-
     var _this;
 
     babelHelpers.classCallCheck(this, Outer);
 
-    var Inner = /*#__PURE__*/function () {
+    var Inner = /*#__PURE__*/function (_this2) {
       function Inner() {
         babelHelpers.classCallCheck(this, Inner);
       }
 
       babelHelpers.createClass(Inner, [{
-        key: _this = _super.call(_this2),
+        key: _this2,
         value: function value() {
           return 'hello';
         }
       }]);
       return Inner;
-    }();
+    }(_this = _super.call(this));
 
     return babelHelpers.possibleConstructorReturn(_this, new Inner());
   }
diff --git a/packages/babel-plugin-transform-classes/test/fixtures/spec/nested-class-super-property-in-key/output.js b/packages/babel-plugin-transform-classes/test/fixtures/spec/nested-class-super-property-in-key/output.js
index 9b3145d21416..bf1411294fe7 100644
--- a/packages/babel-plugin-transform-classes/test/fixtures/spec/nested-class-super-property-in-key/output.js
+++ b/packages/babel-plugin-transform-classes/test/fixtures/spec/nested-class-super-property-in-key/output.js
@@ -25,19 +25,19 @@ var Outer = /*#__PURE__*/function (_Hello) {
     babelHelpers.classCallCheck(this, Outer);
     _this = _super.call(this);
 
-    var Inner = /*#__PURE__*/function () {
+    var Inner = /*#__PURE__*/function (_babelHelpers$get$cal) {
       function Inner() {
         babelHelpers.classCallCheck(this, Inner);
       }
 
       babelHelpers.createClass(Inner, [{
-        key: babelHelpers.get((_thisSuper = babelHelpers.assertThisInitialized(_this), babelHelpers.getPrototypeOf(Outer.prototype)), "toString", _thisSuper).call(_thisSuper),
+        key: _babelHelpers$get$cal,
         value: function value() {
           return 'hello';
         }
       }]);
       return Inner;
-    }();
+    }(babelHelpers.get((_thisSuper = babelHelpers.assertThisInitialized(_this), babelHelpers.getPrototypeOf(Outer.prototype)), "toString", _thisSuper).call(_thisSuper));
 
     return babelHelpers.possibleConstructorReturn(_this, new Inner());
   }
diff --git a/packages/babel-plugin-transform-classes/test/fixtures/spec/relaxed-method-coercion/output.js b/packages/babel-plugin-transform-classes/test/fixtures/spec/relaxed-method-coercion/output.js
index 5d9a2b9a2e46..6379fd21f1c1 100644
--- a/packages/babel-plugin-transform-classes/test/fixtures/spec/relaxed-method-coercion/output.js
+++ b/packages/babel-plugin-transform-classes/test/fixtures/spec/relaxed-method-coercion/output.js
@@ -1,5 +1,5 @@
 // #1649
-var Foo = /*#__PURE__*/function () {
+var Foo = /*#__PURE__*/function (_Symbol, _Symbol2) {
   "use strict";
 
   function Foo() {
@@ -7,11 +7,11 @@ var Foo = /*#__PURE__*/function () {
   }
 
   babelHelpers.createClass(Foo, [{
-    key: Symbol(),
+    key: _Symbol,
     value: function value() {}
   }, {
-    key: Symbol(),
+    key: _Symbol2,
     value: function value() {}
   }]);
   return Foo;
-}();
+}(Symbol(), Symbol());