This talk revolves around Grinberg's classical hamiltonicity criterion. After a brief historical introduction we shall present combinatorial and topological generalisations of this theorem, and derive some consequences. In particular, we extend Zaks' version of the criterion, which encompasses results of Gehner and Shimamoto. If time permits, we shall also discuss so-called 2-planarising 2-factors. This talk is based on joint work with Gunnar Brinkmann.