Vue

HTML

<script src="https://unpkg.com/vue/dist/vue.js"></script>
<script src="https://unpkg.com/vue-router/dist/vue-router.js"></script>

<div id="app">
  <p>
    <router-link to="/home">/home</router-link>
  </p>
  <router-view></router-view>
</div>

Vue

const Home = {
  template: `
    <div class="user">
      <h2>HomeBasic</h2>
      <router-view></router-view>
    </div>
  `
}

const HomeIndex = { template: '<div>HomeIndex</div>' }
const HomeAnotherChild = { template: '<div>HomeAnotherChild</div>' }

const router = new VueRouter({
  routes: [
    { path: '/home', components:{ default: Home},
      children: [
        { path: '/home', component: HomeIndex },
        { path: 'profile', component: HomeAnotherChild }
      ]
    }
  ]
})

const app = new Vue({ router }).$mount('#app')