How do you realign the transformation widget to object?

Sorry that this is such a newbie question, but I just spent an entire night trying to do it. Once I’ve transformed and rotated something, (e.g. a camera), the rotation axis is offset from the direction the camera is actually pointing. This isn’t just a question of using local space or global space rotations. It make it extremely difficult just to do a simple vertical tilt for example. Thanks! -Albert