In this chapter we give a model-based overview of robust surgery scheduling literature. A robust schedule maintains to perform well in case of disturbances affecting the schedule. We distinguish three types of disturbances that affect the surgery schedule. First, internal disturbances, such as variations in surgical time. Second, external disturbances, such as non-elective surgeries. Third, disturbances due to artificial variability, such as unavailable operating rooms. For each of these disturbances, we provide an overview of models, described in literature, which reduce the effect of the disturbance on the schedule by making it robust. Furthermore, we identify relevant open problems.