Event history data are obtained by observing individuals over time, focusing on times of occurrence of certain events and the types of event occurring. A review is given of event history analysis (in continuous time) based on multistate models. Examples of such models include the two-state model for survival data and the competing risks and disability models. The likelihood function for a multistate model is presented using the theory of counting processes with special emphasis on models with piecewise constant transition intensities, nonparametric models, and models for the transition intensities including covariates along the lines of the semiparametric Cox proportional hazards regression model for survival data. Direct models for various marginal features of event history data, such as state occupation probabilities, are also discussed. Finally, the influence of observational patterns on the inference is discussed.