Abstract. Probabilistic model checking is a powerful technique for formally verifying quantitative properties of systems that exhibit stochastic behaviour. Such systems are found in many application domains: for example, probabilistic behaviour may arise due to the presence of failures in unreliable hardware, message loss in wireless communication channels, or the use of randomisation in distributed protocols. This chapter starts with an introduction to the technique of probabilistic model checking. We then survey some recent advances in the area, including controller synthesis, compositional verification, probabilistic real-time systems and parametric model checking. We illustrate the application of the various techniques with a combination of toy examples and descriptions of larger case studies. The chapter concludes with a discussion of some of the key challenges in the field.