This survey is devoted to the statistical analysis of duration models and point processes. The first section introduces specific concepts and definitions for single-spell duration models. Section two is devoted to the presentation of conditional duration models which incorporate the effects of explanatory variables. Competing risks models are presented in the third section. The fourth section is concerned with statistical inference, with a special emphasis on non- and semi-parametric estimation of single-spell duration models. Section 5 sets forth the main definitions for point and counting processes. Section 6 presents important elementary examples of point processes, namely Poisson, Markov and semi-Markov processes. The last section presents a general semi-parametric framework for studying point processes with explanatory variables.