Babel Compile CSS files
The webpack config looks correct.Probably issue with import of CSS, it has to be smtl like that:
import './style.css'; where './' is path.If you want to write CSS for every component, I suggest you take a look CSS Modules https://github.com/css-modules/css-modules
If you are using webpack-dev-middleware you need to ensure you configure it with your webpack config:
const webpack = require('webpack');const webpackDevMiddleware = require('webpack-dev-middleware');const webpackConfig = require('path/to/webpack.config.js');const compiler = webpack(webpackConfig);module.exports = webpackDevMiddleware(compiler, { /* options */ }