A large number of probabilistic earthquake occurrence models are currently available for seismic hazard assessment. This paper reviews the basic assumptions of the various models, summarizes their stochastic representations and discusses the parameters needed for applications. While the Poisson model is one of the most commonly used in practice it is limited in its representation of the physical earthquake driving mechanism and in its characterization of distinct seismicity patterns. From comparisons of the various models, it is observed that while the Poisson model may apply to regions characterized by moderate frequent earthquakes, other stochastic representations such as the Markov and semi-Markov models describe the sequences of events more adequately at regions with large infrequent earthquakes. Regions that have unique seismicity patterns such as clustering foreshock-mainshock-aftershock sequences are better represented by other stochastic models. It is found, however, that some of these models are difficult to implement and rather restrictive primarily because they require a considerable amount of additional data for model parameter estimation.