I am currently using AWS API Gateway + Lambda for the serverless backend of a social traveling startup. It is absolutely awesome: we are few people in IT and it is amazingly simple to manage the whole stuff.
Moreover imho they are mature services at this time, they are flexible enough with enough configuration properties to fulfill a nearly full control of the development experience.
We reduced our service server costs to 1/6th by moving from Heroku to Lambda. And that's not even considering the main benefit of a big computational request not blocking other requests (which is why we moved to it in the first place).
