The lipocalin family is typically composed of small proteins characterized by a range of different molecular recognition properties. Odorant binding proteins (OBPs) are a class of proteins of this family devoted to the transport of small hydrophobic molecules in the nasal mucosa of vertebrates. Among OBPs, bovine OBP (bOBP) is of great interest for its peculiar structural organization, characterized by a domain swapping of its two monomeric subunits. The effect of pressure on unfolding and refolding of native dimeric bOBP and of an engineered monomeric form has been investigated by theoretical and experimental studies under pressure. A coherent model explains the pressure-induced protein structural changes: i) the substrate-bound protein stays in its native configuration up to 330 MPa, where it loses its substrate; ii) the substrate-free protein dissociates into monomers at 200 MPa; and iii) the monomeric substrate-free form unfolds at 120 MPa. Molecular dynamics simulations showed that the pressure-induced tertiary structural changes that accompany the quaternary structural changes are mainly localized at the interface between the monomers. Interestingly, pressure-induced unfolding is reversible, but dimerization and substrate binding can no longer occur. The volume of the unfolding kinetic transition state of the monomer has been found to be similar to that of the folded state. This suggests that its refolding requires relatively large structural and/or hydrational changes, explaining thus the relatively low stability of the monomeric form of this class of proteins.