The well-known and general "compressibility theorem" for pure substances relates kappa(T) = -(partial derivative ln V/partial derivative P)(N,T) to a spatial integral involving the pair correlation function g((2)). The isochoric inherent structure formalism for condensed phases separates g(2) into two fundamentally distinct contributions : a generally anharmonic vibrational part, and a structural relaxation part. Only the former determines kappa(T) for low-temperature crystals, but both operate in the liquid phase. As a supercooled liquid passes downward in temperature through a glass transition, the structural contribution to kappa(T) switches off to produce the experimentally familiar drop in this quantity. The Kirkwood-Buff solution theory forms the starting point for extension to mixtures,with electroneutrality conditions creating simplifications in the case of ionic systems.