In implementing MVC, is there always an explicit set of classes modeling the role of the controller? (particularly interested in C++/Qt usage)

In implementing MVC abstractions, is there always an explicit set of classes for the controller?

I'm particularly interested in the context of Qt / Signal-Slot code. What code goes into the controller class? At the moment, I do all the connect() tying between my model classes and my View classes in a set of controller classes, as well as some data-structure munging (to get view data into the right data structures for the model), but I'm not too sure if this is the right approach.