Sharepoint - SPFx - Cannot find type definition file for 'es6-collections'

This looks like a known issue while upgrading from SPFx 1.3 to 1.4

To fix it, just install the typed definitions of es6-collections as below:

npm install --save @types/es6-collections

Please update your tsconfig.json (in the root of the project). The latest yeoman generator creates it like this:

{
  "compilerOptions": {
    "target": "es5",
    "forceConsistentCasingInFileNames": true,
    "module": "commonjs",
    "jsx": "react",
    "declaration": true,
    "sourceMap": true,
    "experimentalDecorators": true,
    "skipLibCheck": true,
    "typeRoots": [
      "./node_modules/@types",
      "./node_modules/@microsoft"
    ],
    "types": [
      "es6-promise",
      "webpack-env"
    ],
    "lib": [
      "es5",
      "dom",
      "es2015.collection"
    ]
  }
}