The concept of a server is about outdated. Why do you need a server?
Running the code on Google App Engine, Amazon Lambda, Microsoft Azure Functions, IBM Bluemix OpenWhisk or another stateless solution seems much more sensible and logical.
Currently, you can run WordPress on Google App Engine. When you Google the term there are many how to´s and useful information. In the WordPress plugins directory, several solutions will ease the transition to serverless computing. Several companies are running production WordPress sites for customers on Google App Engine. There is still some limitations so it might be a bit early to make the transition.
Guess it’s just a matter of time before WordPress runs on Amazon Lambda as a serverless and stateless app.
Another alternative is to run WordPress on Microsoft Azure Functions. The current WordPress runs better on Unix-like operating systems, but this might change.
The serverless alternative from the computing giant IBM is another option.