  Nernst and magnetization experiments reveal the existence of a large region
of the cuprate phase diagram above the $T_c$ curve in which vorticity and weak
diamagnetism exist without phase coherence. We discuss the implication that the
transition at $T_c$ is caused by the loss of long-range phase coherence caused
by spontaneous vortex creation. Below $T_c$, these measurements provide an
estimate of the depairing field $H_{c2}$ which is found to be very large
(40-100 T depending on doping). We discuss the high-field Nernst and
magnetization results, binding energy, and the phase diagram of hole-doped
cuprates. Some new magnetization results on the vortex liquid in very
underdoped LSCO in the limit $T\to 0$ are reported as well.
