High hydrostatic pressure induces conformational changes in proteins ranging from compression of the molecules to loss of native structure. In this tutorial review we describe how the interplay between the volume change and the compressibility leads to pressure-induced unfolding of proteins and dissociation of amyloid fibrils. We also discuss the effect of pressure on protein folding and free energy landscapes. From a molecular viewpoint, pressure effects can be rationalised in terms of packing and hydration of proteins.