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I first discuss the main assumptions which can be made for multi-state models: the time-homogeneity and semi-Markov assumptions, the problem of choice of the time scale, the assumption of homogeneity of the population and also assumptions about the way the observations are incomplete, leading to truncation and censoring. The influence of covariates and different durations and time-dependent variables are synthesized using explanatory processes, and a general additive model for transition intensities presented. Different inference approaches, including penalized likelihood, are considered. Finally three examples of application in epidemiology are presented and some references to other works are given.