Image registration, in particular medical image registration, has been subject to extensive studies in the past years. Its versatile and important applications have attracted researchers from various branches, including numerical analysts. In this note, we not only give an overview on some new and exiting approaches but also point out some of the mathematical challenges associated with these approaches. Moreover, we explain why variational based methods to image registration naturally lead to large scaled and challenging optimization and hence numerical linear algebra problems. We present various instructive examples and comment on numerical schemes.