The proposed European X-ray Free-Electron Laser source (XFEL) will provide extremely brilliant (B>10³³ ph/s/mm²/mrad²/0.1% bw) and highly coherent X-ray beams. Due to the pulse structure and the unprecedented brightness one will be able 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. X-ray Photon Correlation Spectroscopy (XPCS) measures the temporal changes in a speckle pattern produced when coherent light is scattered by a disordered system and therefore allows the measurement of S(Q,t). This article summarizes important aspects of the scientific case for an XPCS instrument at the planned XFEL. New XPCS setups taking account of the XFEL pulse structure are described. To cite this article: G. Grübel, C. R. Physique 9 (2008).