Jafar Husain does an excellent job of explaining some of the problems netflix has had with REST APIs and why you might want to take a different approach in his introduction to Falcor video. Falcor is tackling some of the same problems as graphql / relay but making trade offs at different points.

https://netflix.github.io/falcor/starter/why-falcor.html

A REST API may be the best decision for a lot of projects but GraphQL and Falcor are solving interesting problems that come up more and more in single page apps of increasing complexity.