This chapter introduces the Conway–Maxwell–Poisson regression model, along with adaptations of the model to account for zero-inflation, censoring, and data clustering. Section 5.1 motivates the consideration and development of the various COM–Poisson regressions. Section 5.2 introduces the regression model and discusses related issues including parameter estimation, hypothesis testing, and statistical computing in R. Section 5.3 advances that work to address excess zeroes, while Section 5.4 describes COM–Poisson models that incorporate repeated measures and longitudinal studies. Section 5.5 focuses attention on the R statistical packages and functionality associated with regression analysis that accommodates excess zeros and/or clustered data as described in the two previous sections. Section 5.6 considers a general additive model based on COM–Poisson. Finally, Section 5.7 informs readers of other statistical computing softwares that are also available to conduct COM–Poisson regression, discussing their associated functionality. The chapter concludes with discussion.