Count data arise in many contexts, from word lengths to traffic volume to number of bids in online auctions, and generally in many event-counting applications. Yet, there is a scarcity of statistical models for such data. The Poisson distribution is the most popular distribution for modeling count data, yet it is constrained by its equi-dispersion assumption, making it less than ideal for modeling real data that often exhibit over-dispersion or under-dispersion. The COM-Poisson distribution is a two-parameter generalization of the Poisson distribution that allows for a wide range of over-dispersion and under-dispersion. It also contains the Bernoulli and geometric distributions as special cases, and as a member of the exponential family has useful statistical properties. This distribution's flexibility and special properties have prompted a fast growth of methodological and applied research in various fields. In this talk, I will introduce the COM-Poisson distribution and regression model and mention several other COM-Poisson models that have been published thus far. I will also describe applications of the COM-Poisson in various areas including disclosure limitation, marketing, transportation and linguistics.