Abstract. Probabilistic model checking is an approach to the formal modelling and analysis of stochastic systems. Over the past twenty five years, the number of different formalisms and techniques developed in this field has grown considerably, as has the range of problems to which it has been applied. In this paper, we identify the main application domains in which probabilistic model checking has proved valuable and discuss how these have evolved over time. We summarise the key strands of the underlying theory and technologies that have contributed to these advances, and highlight examples which illustrate the benefits that probabilistic model checking can bring. The aim is to inform potential users of these techniques and to guide future developments in the field.