We're moving almost the entirety of our backend processes into Lambda. This has given us vast cost savings in terms of pure infrastructure billing - and time worrying about platform and scale. This move has also made our architecture almost entirely event-driven - another huge benefit as our business itself is inherently event-driven.
API Gateway in conjunction with Lambda has allowed us to become 'serverless'. We have a number of API endpoints that range from simple CRUD operations, through to triggering chains of complex background jobs. Like Lambda, this service has released us from getting bogged down in infrastructure management, freeing up huge amounts of time to focus on solving business problems.