Integer-valued autoregressive of order one (INAR(1)) processes are used in modeling non-life insurance claims. This type of model is suitable for claims counting processes with lag-one dependence. Three applications of INAR(1) model in insurance claims are discussed in this talk. Firstly, an INAR(1) process with dynamic heterogeneity is introduced to model the random fluctuations and correlations from year to year. The application of this model to automobile insurance is presented. Secondly, a Poisson INAR(1) process is proposed to model the number of (unclosed) incurred but not reported (IBNR) claims. Properties and predictions are discussed. Both parametric and non-parametric methods are used for estimating model parameters and their performance in terms of accuracy is compared. Finally, a compound model based on a Poisson INAR(1) counting process (for closed IBNR claims) is studied for the total claim payments. Maximum likelihood techniques are applied for estimating model parameters. Predictions and the level of estimation accuracy is examined by simulation studies. This is a joint work with Ting Zhang, Yang Bai and Jinwan Kim.