We report on the synthesis of superconducting single crystals of FeSe and their characterization by x-ray diffraction, magnetization and resistivity. We have performed ac susceptibility measurements under high pressure in a hydrostatic liquid argon medium up to 14GPa and we find that TC increases up to 33-36K in all samples, but with slightly different pressure dependences on different samples. Above 12GPa no traces of superconductivity are found in any sample. We have also performed a room temperature high pressure x-ray diffraction study up to 12GPa on a powder sample, and we find that, between 8.5 and 12GPa, the tetragonal PbO structure undergoes a structural transition to a hexagonal structure. This transition results in a volume decrease of about 16% and is accompanied by the appearance of an intermediate, probably orthorhombic, phase.