The European X-ray free electron laser source (XFEL) will provide highly brilliant (B > 1033 ph/s/mm2/mrad2/0.1% bw) and coherent X-ray beams. The pulse structure and the unprecedented brightness will allow one for the first time to study fast dynamics in the time domain, thus giving direct access to the dynamic response function S(Q, t), instead of S(Q, ω), which is of central importance for a variety of phenomena such as fast non-equilibrium dynamics initiated, e.g. by a short pump pulse. X-ray photon correlation spectroscopy (XPCS) measures the temporal changes in speckle patterns produced when coherent light is scattered by a disordered system and therefore allows to measure S(Q, t). This paper summarizes important aspects of the scientific case for an XPCS instrument at the planned XFEL. Novel XPCS set-ups are illustrated.