A four dimensional integrable system is semitoric if one of the components of the momentum map is proper and generates a circle action. In the case when each fiber of the momentum map of the circle action contains at most one singular point of focus-focus type, called simple, semitoric systems were classified by Pelayo & Vu Ngoc about 10 years ago. We will discuss the classification when the simplicity assumption is not satisfied. This talk is based on joint work with J. Palmer and A. Pelayo, see arXiv:1909.03501