I will discuss spherical black-hole solutions in Einstein-aether theory, a Lorentz-violating gravitational theory consisting of General Relativity with a dynamical unit timelike vector (the "aether") that defines a preferred timelike direction. These are also solutions to the infrared limit of Horava-Lifshitz gravity. Spherical black-hole solutions of the type expected to form by gravitational collapse exist for all parameter values of the two theories where all presently known experimental constraints are satisfied. Outside the metric horizon, the deviations away from the Schwarzschild metric are typically no more than a few percent for most of the explored parameter regions, which makes them difficult to observe with electromagnetic probes, but in principle within reach of future gravitational-wave detectors. Remarkably, the solutions possess a universal horizon, not far inside the metric horizon, that traps waves of any speed relative to the aether. A notion of black hole thus persists in these theories, even in the presence of arbitrarily high propagation speeds.