This chapter deals with situations when the response variable is an integer nonnegative random quantity representing counts. It explains to model count data as functions of several covariates, particularly when the sampling units are clusters. The most important feature is the widespread situations where count data arise. The likelihood function contains all the relevant information about the mechanism that generated the data. The chapter explores the hypothesis testing on regression coefficients and dispersion parameters in count data involve application of the large sample theory of the likelihood inference. The equality of mean and variance of the Poisson distribution places restriction on the applicability of regression model to real-world data. An issue of importance is when empirical variance in the data exceeds the nominal variance under the presumed model. The advantages of linearization-based methods include a relatively simple form of the linearized model that typically can be fit based on only the mean and variance in the linearized model.