The domain structures, dielectric properties, and phase transformation of (001)-oriented $Pb(Mg_{1/3}Nb_{2/3})O_3-x%PbTiO_3$ (PMN-x%PT) crystals for x=20, 30, 35, and 40 mole% have been investigated. PMN-20%PT consists of polar nano-domains (PND) which do not self-assemble into macro-domain plates. PMN-30%PT consists of PNDs which begin to self-assemble into colonies along preferred {110} planes. PMN-35PT consists of miniature polar domains on the nm scale. PMN-40%PT consists of {001} oriented lamella domains on the mm scale that have internal nano-scale heterogeneities. The dielectric properties of poled (001) PMN-x%PT single crystals have been measured for orientations both parallel and perpendicular to the [001] poling direction. The results of the temperature dependence of the dielectric constant and mesh scans for the 30%PT sample demonstrate that the initial monoclinic phase changes to single domain tetragonal phase and to cubic phase with increasing temperature.