The presence of surfaces does not only change the static properties of condensed matter but also the dynamics. It turns out that the dynamic interfacial properties exhibit an even much wider range of phenomena than the corresponding static properties. Due to inherent difficulties both in theory and experiment these phenomena are to a large extent unexplored. The studies of surface spin waves and surface critical dynamics can be used as first steps in gaining experience with dynamics at interfaces. By the combined use of fieldtheoretical calculations and Monte Carlo simulations the surface structure factor for isotropic ferromagnets has been determined which differs strongly from its bulk counterpart. In addition the surface spin wave spectra in isotropic ferromagnets as obtained from computer simulations with specifically devised integrators for the spin dynamics equation of motion turn out to agree quantitatively with mean field predictions. The dependences of these quantities on, e.g., the orientation of the surface, anisotropies in the exchange interaction, and the different dynamics of antiferromagnets present obvious future challenges.