diff --git a/packages/react-scripts/config/polyfills.js b/packages/react-scripts/config/polyfills.js
index 673fb8399b4..c6c00d69a7c 100644
--- a/packages/react-scripts/config/polyfills.js
+++ b/packages/react-scripts/config/polyfills.js
@@ -22,3 +22,12 @@ require('whatwg-fetch');
 // Object.assign() is commonly used with React.
 // It will use the native implementation if it's present and isn't buggy.
 Object.assign = require('object-assign');
+
+// React depends on collection types Map and Set starting in version 16.
+// We will include these dependencies explicitly until specified versions of
+// browsers may be targeted.
+require('core-js/es6/map');
+require('core-js/es6/set');
+
+// React also depends on requestAnimationFrame in version 16 and newer.
+require('raf/polyfill');
diff --git a/packages/react-scripts/package.json b/packages/react-scripts/package.json
index 123f966d035..5458c553f82 100644
--- a/packages/react-scripts/package.json
+++ b/packages/react-scripts/package.json
@@ -30,6 +30,7 @@
     "babel-runtime": "6.26.0",
     "case-sensitive-paths-webpack-plugin": "2.1.1",
     "chalk": "1.1.3",
+    "core-js": "2.5.1",
     "css-loader": "0.28.4",
     "dotenv": "4.0.0",
     "eslint": "4.4.1",
@@ -48,6 +49,7 @@
     "postcss-flexbugs-fixes": "3.2.0",
     "postcss-loader": "2.0.6",
     "promise": "8.0.1",
+    "raf": "3.3.2",
     "react-dev-utils": "^4.1.0",
     "style-loader": "0.18.2",
     "sw-precache-webpack-plugin": "0.11.4",
@@ -58,8 +60,8 @@
     "whatwg-fetch": "2.0.3"
   },
   "devDependencies": {
-    "react": "^15.5.4",
-    "react-dom": "^15.5.4"
+    "react": "^16.0.0",
+    "react-dom": "^16.0.0"
   },
   "optionalDependencies": {
     "fsevents": "1.1.2"