There are currently multiple approaches for building web applications:
1. Server-side only
This is a classical approach where you render pages on the server by a web framework like Ruby on Rails, Django, Express, Play! Framework and etc.
Typical workflow: Build all your business logic, models and view templates on the server in the framework of your choice.
2. Client-side + REST API
UPDATE: There is no misunderstanding. What I meant by client-side only is complete separation of concerns. Your have a REST API server and a client-side application that talks to that server. Depending on your use case, chances are, you will never have a true client-side only application that doesn't connect to a back-end either for authentication or data persistence.
Typical workflow: Spend hours deciding on Angular vs Backbone vs Ember vs X. Then you build your routes, models, views, controllers on the client. After you are done, now build models, controllers, routes on the server. In a way you are doing double amount of work.
I don't know much about using this approach, but if I were to take a guess, you render your views (View of the MVC framework) on the server. As a result you get SEO support plus faster page loads.
On the Hybrid front there is airbnb's rendr that supposedly combines backbone and express together.
Eric Florenzo has posted on his blog today: React: Finally, a great server/client web stack.
The amount of ways to build web applications is just overwhelming. And for someone who's learning web development this can become a problem. How does one decide on which approach to use in order to build their next application?