While Poisson regression serves as a standard tool for modeling the association between a count response variable and explanatory variables, it is well‐documented that this approach is limited by the Poisson model's assumption of data equi‐dispersion. The Conway–Maxwell–Poisson (COM‐Poisson) distribution has demonstrated itself as a viable alternative for real count data that express data over‐ or under‐dispersion, and thus the COM‐Poisson regression can flexibly model associations involving a discrete count response variable and covariates. This work overviews the ongoing developmental knowledge and advancement of COM‐Poisson regression, introducing the reader to the underlying model (and its considered reparametrizations) and related regression constructs, including zero‐inflated models, and longitudinal studies. This manuscript further introduces readers to associated computing tools available to perform COM‐Poisson and related regressions. This article is categorized under: Statistical Models > Linear Models Statistical Models > Generalized Linear Models