A number of predictive relationships derived from regression analysis of strong-motion data are available for horizontal peak acceleration, velocity, and response spectral values. Theoretical prediction of ground motion calls for stochastic source models because source heterogeneities control the amplitude of ground motion at most, if not all, frequencies of engineering interest. Theoretical methods have been developed for estimation of ground-motion parameters and simulation of ground-motion time series. These methods are particularly helpful for regions such, as eastern North America where strong-motion data are sparse. The authors survey the field, first reviewing developments in ground-motion measurement and data processing. The authors then consider the choice of parameters for characterizing strong ground motion and describe the wave-types involved in strong ground motion and the factors affecting ground-motion amplitudes. They conclude by describing methods for predicting ground motion.