We investigate the high-pressure phase transitions in BiFeO3 by single crystal and powder x-ray diffraction, as well as single crystal Raman spectroscopy. Six phase transitions are reported in the 0-60 GPa range. At low pressures, up to 15 GPa, 4 transitions are evidenced at 4, 5, 7 and 11 GPa. In this range, the crystals display large unit cells and complex domain structures, which suggests a competition between complex tilt systems and possibly off-center cation displacements. The non polar P nma phase remains stable over a large pressure range between 11 and 38 GPa, where the distortion (tilt angles) changes only little with pressure. The two high-pressure phase transitions at 38 and 48 GPa are marked by the occurence of larger unit cells and an increase of the distorsion away from the cubic parent perovskite cell. We find no evidence for a cubic phase at high pressure, nor indications that the structure tends to become cubic. The previously reported insulator-to-metal transition at 50 GPa appears to be symmetry breaking.