The derivations of equations of state to describe the volume-pressure variation of a solid are based upon certain assumptions about the properties of the solid. For finite strain equations of state, these assumptions include homogeneity and isotropy of the strain distribution in the sample, the continuous differentiability of the equation of state parameters with respect to extensive variables, and the assumption that terms involving higher-order powers of the finite strain do not contribute significantly to the free energy of the material. We examine these assumptions and demonstrate that, within the experimental uncertainties, crystalline solids with no or limited degrees of internal structural freedom compress in the manner predicted by finite strain equations of state, even though in some cases the assumptions involved in the derivation of the equation of state are demonstrably violated. In more complex structures with a larger number of degrees of structural freedom, a variety of behaviour is observed; most undergo continuous structural change with increasing pressure and the evolution of the volume with pressure again follows that predicted by the finite strain equations of state. However, a significant number of complex structures undergo changes in compression mechanism which, in some cases, result in significant deviations from the behaviour predicted by the equations of state.