The author shows how to expand critical amplitudes in inverse powers of the dimensionality d. The technique, which is rather general, is applied to the classical n-vector model, with particular emphasis on the self-avoiding walk (n=0) and Ising (n=1) cases. The existence of these expansions and of similar ones for critical points and critical constants suggests that 1/d expansions for non-universal quantities are analogous to the epsilon expansions for universal quantities.