Cyber security is an important concern for all individuals, organisations and governments globally. Cyber attacks have become more sophisticated, frequent and dangerous than ever, and traditional anomaly detection methods have been proved to be less effective when dealing with these new classes of cyber threats. In order to address this, both classical and Bayesian models offer a valid and innovative alternative to the traditional signature-based methods, motivating the increasing interest in statistical research that it has been observed in recent years. In this review we provide a description of some typical cyber security challenges, typical types of data and statistical methods, paying special attention to Bayesian approaches for these problems.