Mouse move inside control/Widget

I'm a Qt newbie whos first job is to port a Borland Builder C++ project to Qt for portability.

First thing to do doesn't seem to be in Qt by default - mouse movement inside control (Widgets?). Basically, draw a QButton onto a form (Window?) and then let the user click the left mouse button on it and drag the button around the form.

What used to happen:
User clicks left button - get WM_LBUTTONDOWN
User moves mouse whilst button is down - get lots of WM_MOUSEMOVE which are then translated to screen co-ords and then from screen co-ords into form co-ords so the button can move in relation to the form. The offset into the control/widget is taken at LBUTTONDOWN time so the control doesn't jerk when you first move the mouse.

Since Qt is multi platform I'm guessing theres no window messages any more, and although there are "slots" which allow you to do things like "on mouse click", there doesn't seem to be a "on mouse move" slot.