In this talk we will present several new results regarding what invertible linear operators can do to frames. We will start by characterizing the operators which send a given frame to a frame with the same frame operator. This leads to a new definition of equivalence of frames. We then turn our attention to the following question: When can we find an invertible linear operator which sends some fixed frame to an equal norm frame. First we will characterize the frames for which such operators exist, then we proceed to characterize these operators. We will conclude by presenting a new characterization of Parseval frames.