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This text provides graduate students and researchers with an up-to-date survey of econometric and statistical techniques for the analysis of count data, with a focus on regression models. Specialised discrete data probability models are required in order to interpret results in terms of an underlying structural process, and to use the model for predicting the distribution of outcomes. The book starts with a presentation of the benchmark Poisson regression model. Alternative models address unobserved heterogeneity, state dependence, selectivity, endogeneity, underreporting, and clustered sampling. Testing and estimation is discussed, including Bayesian inference. Finally, applications are reviewed in fields such as economics, marketing, sociology, demography, and health sciences.