Let G be a reductive linear algebraic group. Serre has defined a notion of G-complete reducibility for subgroups of G. If G = GL(V), then a subgroup H is G-completely reducible if and only if V is completely reducible as an H-module. In this talk I will explore some properties of G-complete reducibility; in particular, how it can be linked with the complete reducibility of modules, even when there is no “natural” module for G.