The occurrence of potentially hazardous geologic events such as landslides, rock falls, earthquakes, floods, and debris flows can be predicted using two fundamentally different approaches: deterministic and probabilistic. The most significant difference between the two approaches to geologic hazard assessment is whether a process is envisioned to be the result of an exact causal relationship or if some element of random behavior is assumed to be part of the system. Although the assumption of random behavior may seem self-defeating, it can provide a useful tool for the solution of important problems as long as the randomness can be quantified using statistical models. Each of these two methods can be approached either rationally (sing models derived from accepted physical or chemical principles) or empirically (by studying the occurrence of events without explicit regard to their driving mechanism). The complexity of the geologic process commonly dictates which approach is used for a particular problem, ranging from rational deterministic models for relatively simple systems such as small landslides to empirical probabilistic models for complicated processes such as floods and earthquakes. Examples of each type of model are discussed throughout the paper, primarily within the context of slope stability and the recurrence of extreme events such as floods.