Although the INGARCH models for count time series are said to be an integervalued counterpart to the generalized autoregressive conditional heteroskedasticity (GARCH) models, they may also be understood as an adaption of the autoregressive movingaverage (ARMA) models to the countdata case. The stochastic properties of these models as well as some extensions are discussed. In particular, the INGARCH models that are a type of linear conditional regression model, and also nonlinear regression models have been proposed for count time series.