Since the 1930s, when the pseudo-static analysis methods were introduced for the seismic design of concrete and embankment dams, the following major developments have taken place: (i) change from pseudo-static to dynamic seismic analysis of dams, (ii) change from the representation of the earthquake ground shaking by a seismic oefficient to safety evaluation earthquake ground motion parameters, (iii) change from single ground shaking hazard to multiple seismic hazards including mass movements, and faulting, and (iv) change from safety factor and allowable stress concepts to rational seismic performance criteria, characterized mainly by dam deformations. There are still considerable uncertainties about the behavior of dams under strong ground shaking. For the seismic safety assessment of dams stress and deformation analyses and dynamic stability analyses are usually required. The bases of any numerical analysis are seismic design and safety criteria. Today, according to ICOLD Bulletin 148 “Selecting Seismic Parameters for Large Dams” two levels of earthquake ground motion are specified for new dams, i.e. the operating basis earthquake (OBE) and safety evaluation earthquake (SEE) ground motions. For existing dams the safety check may only be required for the SEE. The seismic design criteria, the seismic load combinations and the seismic performance and safety criteria of new and existing dams are discussed and recommendations are made for the seismic safety evaluation of existing dams, which were designed using outdated seismic design criteria and methods of seismic analysis.