Repair is a type of maintenance carried out on an item after it fails. A failure may occur any time, hence the times to repair cannot be pre-specified. Methods used to model times to failures are normally stochastic processes such as the renewal process and the homogeneous Poisson process, depending on the effectiveness of a repair. Apparently, the effectiveness of repair will in turn affect the probability of failures. As such, there have been developed many stochastic processes to model the failure processes in the literature. This paper reviews existing failure process models and discusses future development that is needed.