On the Laravel News site there's a new tutorial posted showing you how to create a Vue.js single page application with Laravel for when you have API-driven applications.

Building a Vue single page application (SPA) with Laravel is a beautiful combination for building clean API-driven applications. In this tutorial, we show you how to get up and running with Vue router and a Laravel backend for building a SPA. We will focus on the wiring up all the pieces needed, and then in a follow-up tutorial, we will further demonstrate using Laravel as the API layer.

They walk you through the creation of a simple SPA that will render the initial content and allow for the browsing back and forth between content without a page reload. The tutorial helps you get all required libraries installed and includes the code to define the Vue router and two routes. The contents of the .vue files are also included as well as the server-side code to power the application.