The cohomological dimension of a torsion-free group is a very useful invariant, which can be defined both algebraically and (modulo a notorious open problem in dimen- sion 2) geometrically. For groups containing torsion, the ‘correct’ notion of dimension is less clear, which prompted K S Brown’s question in 1977. I shall discuss the history (and pre-history) of this question and some recent joint work with Nansen Petrosyan on this topic.