The Langevin equation is widely used to model coarse-grained dynamics of soft and biological materials. However, it is not obvious for which systems and which processes the Langevin equation predicts a good approximation to the true dynamics. In this talk we will give an introduction to projection operator formalisms as a tool to systematically coarse-grain dynamics. We will show under which approximations the Langevin equation can be obtained from the dynamics of the underlying microscopic system and in which cases it makes sense to introduce a potential of mean force. We demonstrate the implications of our derivation for the structure of memory terms and for generalized fluctuation-dissipation relations. We show, in particular, that the widely used, simple structure which contains a potential of mean force, a memory term which is linear in the observable, and a fluctuating force which is related to the memory term by a fluctuation-dissipation relation, is neither exact nor can it, in general, be derived as a controlled approximation to the exact dynamics.