The INARMA models for count time series constitute an integervalued counterpart to the conventional autoregressive movingaverage (ARMA) models. They adapt the ARMA recursion to the countdata case using an appropriate thinning operation, for example, binomial thinning. The basic INARMA models have stochastic properties being analogous to those of the stationary ARMA models, and also several extensions have been developed. In particular, there exist modifications of the INARMA approach to deal with bounded counts or multivariate counts.