Although highly valuable for a variety of applications, urban mobility data is rarely made openly available as it contains sensitive personal information. Synthetic data aims to solve this issue by generating artificial data that resembles an original dataset in structural and statistical characteristics, but omits sensitive information. For mobility data, a large number of corresponding models have been proposed in the last decade. This systematic review provides a structured comparative overview of the current state of this heterogeneous, active field of research. A special focus is put on the applicability of the reviewed models in practice.