There is a wide range of tabular data of great value to science, economy and social progress. When sharing such data, privacy must be taken into account. Traditionally, this has been addressed through anonymization. However, in recent years, with the growth of AI, the possibility of using generative models has emerged as a way to generate synthetic data that guarantees privacy while maintaining their utility. This systematic literature review aims to identify and classify existing privacy-preserving tabular generative models in order to create a taxonomy of solutions. In addition, we analyze the privacy metrics and techniques they use, and identify possible unexplored lines of research.