Gruntfile.js

'use strict';

var mountFolder = function (connect, dir) {
  return connect.static(require('path').resolve(dir));
};

var webpackDistConfig = require('./webpack.dist.config.js'),
    webpackDevConfig = require('./webpack.config.js');

module.exports = function (grunt) {
  // Let *load-grunt-tasks* require everything
  require('load-grunt-tasks')(grunt);

  // Read configuration from package.json
  var pkgConfig = grunt.file.readJSON('package.json');

  grunt.initConfig({
    pkg: pkgConfig,

    webpack: {
      options: webpackDistConfig,
      dist: {
        cache: false
      }
    },

    'webpack-dev-server': {
      options: {
        hot: true,
        port: 8000,
        webpack: webpackDevConfig,
        publicPath: '/assets/',
        contentBase: './<%= pkg.src %>/'
      },

      start: {
        keepAlive: true
      }
    },

    connect: {
      options: {
        port: 8000
      },

      dist: {
        options: {
          keepalive: true,
          middleware: function (connect) {
            return [
              mountFolder(connect, pkgConfig.dist)
            ];
          }
        }
      }
    },

    open: {
      options: {
        delay: 500
      },
      dev: {
        path: 'http://localhost:<%= connect.options.port %>/webpack-dev-server/'
      },
      dist: {
        path: 'http://localhost:<%= connect.options.port %>/'
      }
    },

    copy: {
      dist: {
        files: [
          // includes files within path
          {
            flatten: true,
            expand: true,
            src: ['<%= pkg.src %>/*'],
            dest: '<%= pkg.dist %>/',
            filter: 'isFile'
          },
          {
            flatten: true,
            expand: true,
            src: ['<%= pkg.src %>/images/*'],
            dest: '<%= pkg.dist %>/images/'
          }
        ]
      }
    },

    clean: {
      dist: {
        files: [{
          dot: true,
          src: [
            '<%= pkg.dist %>'
          ]
        }]
      }
    }
  });

  grunt.registerTask('serve', function (target) {
    if (target === 'dist') {
      return grunt.task.run(['build', 'open:dist', 'connect:dist']);
    }

    grunt.task.run([
      'open:dev',
      'webpack-dev-server'
    ]);
  });

  grunt.registerTask('build', ['clean', 'copy', 'webpack']);

  grunt.registerTask('default', []);
};

webpack.config.js

/*
 * Webpack development server configuration
 *
 * This file is set up for serving the webpack-dev-server, which will watch for changes and recompile as required if
 * the subfolder /webpack-dev-server/ is visited. Visiting the root will not automatically reload.
 */
'use strict';
var webpack = require('webpack');

module.exports = {
  output: {
    filename: 'main.js',
    publicPath: '/assets/'
  },

  cache: true,
  debug: true,
  devtool: false,
  entry: [
    'webpack/hot/only-dev-server',
    './src/components/main.js'
  ],

  stats: {
    colors: true,
    reasons: true
  },

  resolve: {
    extensions: ['', '.js', '.jsx'],
    alias: {
      'styles': __dirname + '/src/styles',
      'mixins': __dirname + '/src/mixins',
      'components': __dirname + '/src/components/',
      'stores': __dirname + '/src/stores/',
      'actions': __dirname + '/src/actions/'
    }
  },
  module: {
    preLoaders: [{
      test: /\.(js|jsx)$/,
      exclude: /node_modules/,
      loader: 'jsxhint'
    }],
    loaders: [{
      test: /\.(js|jsx)$/,
      exclude: /node_modules/,
      loader: 'react-hot!babel-loader'
    }, {
      test: /\.css$/,
      loader: 'style-loader!css-loader'
    }, {
      test: /\.json$/,
      loader: 'json-loader'
    }, {
      test: /\.(png|jpg|woff|woff2)$/,
      loader: 'url-loader?limit=8192'
    }]
  },

  plugins: [
    new webpack.HotModuleReplacementPlugin(),
    new webpack.NoErrorsPlugin()
  ]
};

I'm running grunt serve