CAT(0) cube complexes have become a major player in geometric group theory, thanks to a combination of two factors: they are rigid enough to give useful information about groups that act on them; but they are flexible enough to allow many groups to do so. The main tool for building actions on CAT(0) cube complexes is Sageev's construction. In this talk, I'll discuss Sageev's construction, and describe a generalisation of it that allows one to construct group actions other types of metric space of interest. Based on joint work with Abdul Zalloum and Davide Spriano.