Functional Form and Heterogeneity in Models for Count Data surveys practical extensions of the Poisson and negative binomial (NB) models that practitioners can employ to refine the specifications or broaden their reach into new situations. The author resolves some inconsistencies of the panel data models with other more familiar results for the linear regression model. It focuses on two large issues: the accommodation of overdispersion and heterogeneity in the basic count framework and the functional form of the conditional mean and the extension of models of heterogeneity to models for panel data and sources of correlation across outcomes. The first is more straightforward since, in principle, these are elements of the conditional variance of the distribution of counts that can be analyzed apart from the conditional mean. Robust inference methods for basic models can be relied upon to preserve the validity of estimation and inference procedures. The second feature motivates the development of more intricate models such as the two part, panel and bivariate models presented in the text.