Since the early work of Lehoczky on real-time queuing theory, probabilistic approaches have addressed many aspects of real-time systems. This presentation concentrates on the migration of probabilistic methods from modelling soft real-time systems to analysing hard real-time systems. The history of this migration is outlined over the last two decades, advancing under different banners including stochastic, probabilistic and statistical analysis. Here, the shift from the deterministic analysis of single upper bound values to more expressive forms using probability distributions has undermined or modified many classical real-time results, such as the optimality of Rate Monotonic assignment. Two common misconceptions concerning probabilistic real-time systems are discussed: independence and the identical distribution. These properties are less restrictive than is widely appreciated and together with probabilistic worst-case reasoning form the basis of the main results currently proposed for hard real-time systems. The presentation summarises recent state-of-the-art research into probabilistic real-time systems, and concludes with the main open challenges in this area.