Modest pressures encountered in the biosphere (i.e., below a few kbar) have extraordinary effects on biomembranes and proteins. These include pressure denaturation of proteins, dramatic changes in protein-protein association, substrate binding, membrane ion transport, DNA transcription, virus infectivity, and enzyme kinetics. Yet all of the biomaterials involved are highly incompressible. The challenge to the physicist is to understand the structural coupling between these effects and pressure to elucidate the relevant mechanisms. X-ray diffraction studies of membranes and proteins under pressure will be described. It is seen that it is not so much the magnitude of the changes, but rather the differential compressibilities of different parts of the structure that are responsible for effects.