Serverless computing: Amazon Lambda
Amazon AWS pioneered the idea of serverless computing. The basic idea is to eliminate servers altogether, and instead tie pieces of code to events that may occur (such as receiving a web request at a particular address). The code is executed when the event occurs; databases may be updated, APIs may be called, and results may be returned, but the computing instance ceases to exist as soon as the code returns.
The main benefit of serverless computing is that there is no need to install, configure, patch, monitor, and maintain a server. Furthermore, costs are only incurred when the code is actually executing based on the resources it consumes. Thus, for operations that are triggered fairly infrequently, the cost savings can be substantial.