I prefer the term "Services" over "Operations".

Services is where the logic of your application should live, and services should be HTTP (or any protocol) agnostic. They should only speak in models and native types, and should abstract all of your logic away from your controllers and models.

This leaves the controllers as a thin http handling layer that parses inputs and then lets the service handle the work.

The response from the service is then transformed appropriately (JSON, HTML, etc) and sent back to the caller.

Just my $0.02