This handbook presents state-of-the-art methods for modeling time series of counts and incorporates frequentist and Bayesian approaches for discrete-valued spatio-temporal data and multivariate data. The book examines the advantages and limitations of the various modeling techniques and keeps probabilistic, technical details to a minimum. While the book focuses on time series of counts, some of the methods discussed can be applied to other types of discrete-valued time series, such as binary-valued or categorical time series.