Building modular javascript applications in ES6 with React, Webpack and Babel

So, you have decided to build your new javascript application using React and you also want to use that new fancy ES6 syntax in it. In addition you want to create reusable components and publish them to NPM. How exactly can you do this today? How do you publish ES6 to NPM and use it in your project later? It took me a while to nail all the bits and pieces, so I thought I’d share my knowledge here.