We have studied the structural behavior of bismuth phosphate under compression. We performed x-ray powder diffraction measurements up to 31.5 GPa and ab initio calculations. Experiments were carried out on different polymorphs; trigonal (phase I) and monoclinic (phases II and III). Phases I and III, at low pressure (0.2-0.8 GPa), transform into phase II, which has a monazite-type structure. At room temperature, this polymorph is stable up to 31.5 GPa. Calculations support these findings and predict the occurrence of an additional transition from the monoclinic monazite-type to a tetragonal scheelite-type structure (phase IV). This transition was experimentally found after the simultaneous application of pressure (28 GPa) and temperature (1500 K), suggesting that at room temperature the transition might by hindered by kinetic barriers. Calculations also predict an additional phase transition at 52 GPa, which exceeds the maximum pressure achieved in the experiments. This transition is from phase IV to an orthorhombic barite-type structure (phase V). We also studied the axial and bulk compressibility of BiPO4. Room-temperature pressure-volume equations of state are reported. BiPO4 was found to be more compressible than isomorphic rare-earth phosphates. The discovered phase IV was determined to be the less compressible polymorph of BiPO4. On the other hand, the theoretically predicted phase V has a bulk modulus comparable with that of monazite-type BiPO4. Finally, the isothermal compressibility tensor for the monazite-type structure is reported at 2.4 GPa showing that the direction of maximum compressibility is in the (010) plane at approximately 15 (21) degrees to the a axis for the case of our experimental (theoretical) study.