The devastating consequences of the 2004 Indian Ocean and 2011 Tohoku-oki tsunamis have led to increased research into many different aspects of the tsunami phenomenon. In this paper, we review research related to the observed complexity and uncertainty associated with tsunami generation, propagation, and occurrence described and analyzed using a variety of stochastic models. In each case, tsunamis generated by earthquakes are primarily considered. Stochastic models are developed from the physical theories that govern tsunami evolution combined with empirical models fitted to seismic and tsunami observations, as well as tsunami catalogs. These stochastic models are key to providing probabilistic forecasts and hazard assessments for tsunamis. The stochastic methods described here are similar to those described for earthquakes (Vere-Jones, 2013) and volcanoes (Bebbington, 2013) in this Encyclopedia.