diff --git a/package.json b/package.json
index 198855b6ca1..ac8d1c0e8db 100644
--- a/package.json
+++ b/package.json
@@ -19,7 +19,7 @@
     "compile:lockfile": "node tasks/compile-lockfile.js"
   },
   "devDependencies": {
-    "eslint": "5.15.1",
+    "eslint": "5.16.0",
     "execa": "1.0.0",
     "fs-extra": "^7.0.1",
     "get-port": "^4.2.0",
diff --git a/packages/babel-preset-react-app/create.js b/packages/babel-preset-react-app/create.js
index 74514baa653..b645a22ede2 100644
--- a/packages/babel-preset-react-app/create.js
+++ b/packages/babel-preset-react-app/create.js
@@ -81,6 +81,9 @@ module.exports = function(api, opts, env) {
         {
           // Allow importing @babel/polyfill in entrypoint and use browserlist to select polyfills
           useBuiltIns: 'entry',
+          // Set the corejs version we are using to avoid warnings in console
+          // This will need to change once we upgrade to corejs@3
+          corejs: 2,
           // Do not transform modules to CJS
           modules: false,
           // Exclude transforms that make all code slower
diff --git a/packages/babel-preset-react-app/package.json b/packages/babel-preset-react-app/package.json
index 90c8a7714e5..6591de25ef5 100644
--- a/packages/babel-preset-react-app/package.json
+++ b/packages/babel-preset-react-app/package.json
@@ -17,24 +17,24 @@
     "test.js"
   ],
   "dependencies": {
-    "@babel/core": "7.3.4",
-    "@babel/plugin-proposal-class-properties": "7.3.4",
-    "@babel/plugin-proposal-decorators": "7.3.0",
-    "@babel/plugin-proposal-object-rest-spread": "7.3.4",
+    "@babel/core": "7.4.3",
+    "@babel/plugin-proposal-class-properties": "7.4.0",
+    "@babel/plugin-proposal-decorators": "7.4.0",
+    "@babel/plugin-proposal-object-rest-spread": "7.4.3",
     "@babel/plugin-syntax-dynamic-import": "7.2.0",
-    "@babel/plugin-transform-classes": "7.3.4",
-    "@babel/plugin-transform-destructuring": "7.3.2",
-    "@babel/plugin-transform-flow-strip-types": "7.3.4",
+    "@babel/plugin-transform-classes": "7.4.3",
+    "@babel/plugin-transform-destructuring": "7.4.3",
+    "@babel/plugin-transform-flow-strip-types": "7.4.0",
     "@babel/plugin-transform-react-constant-elements": "7.2.0",
     "@babel/plugin-transform-react-display-name": "7.2.0",
-    "@babel/plugin-transform-runtime": "7.3.4",
-    "@babel/preset-env": "7.3.4",
+    "@babel/plugin-transform-runtime": "7.4.3",
+    "@babel/preset-env": "7.4.3",
     "@babel/preset-react": "7.0.0",
     "@babel/preset-typescript": "7.3.3",
-    "@babel/runtime": "7.3.4",
+    "@babel/runtime": "7.4.3",
     "babel-loader": "8.0.5",
     "babel-plugin-dynamic-import-node": "2.2.0",
-    "babel-plugin-macros": "2.5.0",
+    "babel-plugin-macros": "2.5.1",
     "babel-plugin-transform-react-remove-prop-types": "0.4.24"
   }
 }
diff --git a/packages/react-dev-utils/package.json b/packages/react-dev-utils/package.json
index b1495553456..ed947d1148d 100644
--- a/packages/react-dev-utils/package.json
+++ b/packages/react-dev-utils/package.json
@@ -48,7 +48,7 @@
   "dependencies": {
     "@babel/code-frame": "7.0.0",
     "address": "1.0.3",
-    "browserslist": "4.4.2",
+    "browserslist": "4.5.4",
     "chalk": "2.4.2",
     "cross-spawn": "6.0.5",
     "detect-port-alt": "1.1.6",
@@ -69,7 +69,7 @@
     "recursive-readdir": "2.2.2",
     "shell-quote": "1.6.1",
     "sockjs-client": "1.3.0",
-    "strip-ansi": "5.1.0",
+    "strip-ansi": "5.2.0",
     "text-table": "0.2.0"
   },
   "devDependencies": {
diff --git a/packages/react-error-overlay/package.json b/packages/react-error-overlay/package.json
index 89dc73d2f2b..f24efd368d9 100644
--- a/packages/react-error-overlay/package.json
+++ b/packages/react-error-overlay/package.json
@@ -31,7 +31,7 @@
   ],
   "devDependencies": {
     "@babel/code-frame": "7.0.0",
-    "@babel/core": "7.3.4",
+    "@babel/core": "7.4.3",
     "anser": "1.4.8",
     "babel-eslint": "10.0.1",
     "babel-jest": "24.7.1",
@@ -40,7 +40,7 @@
     "chalk": "^2.4.2",
     "chokidar": "^2.1.2",
     "cross-env": "5.2.0",
-    "eslint": "5.15.1",
+    "eslint": "5.16.0",
     "eslint-config-react-app": "^3.0.8",
     "eslint-plugin-flowtype": "2.50.1",
     "eslint-plugin-import": "2.16.0",
@@ -49,7 +49,7 @@
     "flow-bin": "^0.63.1",
     "html-entities": "1.2.1",
     "jest": "24.7.1",
-    "jest-fetch-mock": "2.1.1",
+    "jest-fetch-mock": "2.1.2",
     "object-assign": "4.1.1",
     "promise": "8.0.2",
     "raw-loader": "^1.0.0",
diff --git a/packages/react-scripts/package.json b/packages/react-scripts/package.json
index e8773271fef..380c09991c7 100644
--- a/packages/react-scripts/package.json
+++ b/packages/react-scripts/package.json
@@ -24,10 +24,10 @@
   },
   "types": "./lib/react-app.d.ts",
   "dependencies": {
-    "@babel/core": "7.3.4",
+    "@babel/core": "7.4.3",
     "@svgr/webpack": "4.1.0",
-    "@typescript-eslint/eslint-plugin": "1.4.1",
-    "@typescript-eslint/parser": "1.4.1",
+    "@typescript-eslint/eslint-plugin": "1.6.0",
+    "@typescript-eslint/parser": "1.6.0",
     "babel-eslint": "10.0.1",
     "babel-jest": "24.7.1",
     "babel-loader": "8.0.5",
@@ -37,7 +37,7 @@
     "css-loader": "2.1.1",
     "dotenv": "6.2.0",
     "dotenv-expand": "4.2.0",
-    "eslint": "5.15.1",
+    "eslint": "5.16.0",
     "eslint-config-react-app": "^3.0.8",
     "eslint-loader": "2.1.2",
     "eslint-plugin-flowtype": "2.50.1",