Regression models for count data are attracting increasing attention in many fields of application, among them health economics, ecological modeling and political science. It has emerged that the classical regression models (Poisson and Negative Binomial) are often not flexible enough in empirical work, hence various generalizations and modifications have been proposed. However, many aspects of these new models are still not well understood. The project investigates properties of generalized count data regression models, with an emphasis on computational aspects. It is planned to also implement various count data tools in the R system for statistical computing.