Where is the UI code in MVC pattern for application dev?

I've read up on MVC but am still unclear on whether there is a consensus whether the UI code (e.g., Qt) is part of the Viewer or the Controller. If I'm understanding some descriptions, the Viewer displays the model but the user interfaces directly with the controller, which I interpret as the UI is part of the controller. Other descriptions suggest the Viewer is for input and output, so contains all the UI code, freeing the controller to only handle the logic.

Are there two schools of thought on whether the UI code belongs in the Viewer or the Controller? If not, which one gets the UI code?