Dielectric permittivities, polarization-electric-field hysteresis loops, and domain structures have been measured as a function of temperature in relaxor-based ferroelectric single crystals (PbMg 1/3 Nb 2/3 O 3 ) 0.68 (PbTiO 3 ) 0.32 ͑PMN-32%PT͒ for ͗110͘ cub and ͗211͘ cub orientations. Contrary to the pure PbMg 1/3 Nb 2/3 O 3 ͑PMN͒, PMN-32%PT exhibits apparent crystallographic orientation dependences of dielectric permittivities, polarizations, domain structures and phase transitions. With a prior field-cooled treatment, a field-induced state, perhaps of orthorhombic symmetry, is evidenced and coexists with the rhombohedral symmetry in the low-temperature region. This field-induced phase is manifested by an extra dielectric peak observed near 373 K for the ͗211͘ cub orientation. A relaxation mechanism which is responsible for the so-called diffuse phase transition crosses a wide temperature region of ϳ340-400 K and results from fluctuations between rhombohedral and tetragonal states. In order of increasing temperature ͑without a prior field-cooled treatment͒, PMN-32%PT undergoes successive phase transformations: rhombohedral phase→coexistence of rhombohedral and tetragonal phases→tetragonal phase→coexistence of tetragonal and cubic phases→cubic phase.