This survey covers schedulability analysis techniques for probabilistic real-time systems. It reviews the key results in the field from its origins in the late 1980s to the latest research published up to the end of August 2018. The survey outlines fundamental concepts and highlights key issues. It provides a taxonomy of the different methods used, and a classification of existing research. A detailed review is provided covering the main subject areas as well as research on supporting techniques. The survey concludes by identifying open issues, key challenges and possible directions for future research.