The radial collapse of a homogeneous disk of collisionless particles can be solved analytically in Newtonian gravitation. To solve the problem in general relativity, however, requires the full machinery of numerical relativity. The collapse of a disk is the simplest problem that exhibits the two most significant and challenging features of strong-field gravitation: black hole formation and gravitational wave generation. We carry out dynamical calculations of several different relativistic disk systems. We explore the growth of ring instabilities in equilibrium disks, and how they are suppressed by sufficient velocity dispersion. We calculate wave forms from oscillating disks, and from disks that undergo gravitational collapse to black holes. Studies of disk collapse to black holes should also be useful for developing new techniques for numerical relativity, such as apparent horizon boundary conditions for black hole spacetimes.