In the framework of finite group theory, many results confirm that the set of conjugacy class sizes provides significant information about the structure of a group. Nonetheless, some properties cannot be determined from this piece of information: for example, the group order is unknown; less trivially, solubility and nilpotency cannot be detected. By considering the multiset of class sizes, i.e. taking their frequencies into account, some of these properties can be determined. The purpose of this seminar is to review results within this research line, and to present recent progress from a local point of view.