The phase diagram and electrical transport properties of strongly type-II superconductors are examined in the presence of thermal fluctuations and random vortex pinning. Pinning destroys the vortex lattice phase, probably replacing it with a vortex glass phase that has spin-glass like off-diagonal order and strictly zero resistivity in contrast to the conventional picture. The properties of this novel phase and the phase transition into it are summarized and experiments on YBa2Cu3O7 and Bi2Sr2CaCu2O8 are discussed in light of the results. The latter is argued to exhibit quasi-two-dimensional behavior over a wide range of temperature and magnetic field. © 1991.