We're not exactly heavily oriented towards a microservice architecture, but we do use them a fair bit for some resource intensive methods. I'm pretty happy with Azure Functions, especially with the parts that I can automate: I'll describe how to setup a simple Jenkins job that builds your function and deploys it automatically to Azure Functions.
In your projects repository, you need a build script to compile your function, like this:
It's not too complicated, but I want to highlight these points:
In Jenkins, you simply call this script and provide the required parameters:
I really encourage you to use something like the Credentials Binding Plugin to provide your secrets. Otherwise, it's as simple as a setup can be. You can set up Git Hooks or use the GitHub plugin to automatically build whenever you push new code.
If you're wondering where to actually get your deployment credentials, they're included in the Publishing Profile that you can download for the function in the Azure portal.