I've been working with AWS Lambda recently and I am very impressed. Usually if I need to set up a microservice or a recurring task or anything like that I'll just set up something on one of my virtual servers so I didn't think Lambda would be all that useful. But it makes it really, really easy to set up little tasks and it is much cheaper than having a whole virtual server.
You can create tasks in a number of different languages, and set up a variety of triggers ranging from HTTP requests to scheduled tasks, and when the Lambda is triggered AWS spins it up, executes it and then shuts it down. Since it is so ephemeral it is completely stateless, but you can load files from S3 buckets if you need data of any sort. I assume you can probably also connect to a variety of AWS databases as well, although I haven't done this yet. If you need additional libraries or packages that are not default you can create a layer containing them.
Lambda is not going to replace servers for most use cases, but I think serverless technology is going to make quite a dent in the near future.