This report presents a comprehensive review of the state of the art of probabilistic seismic hazard analysis. This type of analysis essentially provides information regarding the likelihood that various levels of a ground motion parameter will be exceeded in a given period of time. The report begins with a discussion of the various seismic parameters required for the analysis and the calculation of these parameters based on seismic history data. Problems involved in the estimation of these parameters exclusively on the basis of seismological data are outlined, and emphasis is placed on the need to utilize and incorporate geologic and geophysical information in the analysis. A brief presentation of Baye's theorem and discussion of the procedure for seismic hazard estimation using the theorem are provided. The report continues with a presentation of the various mathematical formulations used in the calculation of seismic hazard probabilities. This section also includes a discussion of the use of computer programs to facilitate the calculations involved in the analysis. Concluding the report is a presentation and discussion of the various practical applications of seismic hazard analysis, emphasizing use in structural and geotechnical engineering. Some recent seismic hazard maps for the U.S. incorporating probability calculations are presented and reviewed in this section. (Author).