High-velocity clouds (HVCs) consist of neutral hydrogen (HI) at velocities incompatible with a simple model of differential galactic rotation; in practice one uses v LSR 90 km/s to define HVCs. This review describes the main features of the sky and velocity distributions, as well as the available information on cloud properties, small-scale structure, velocity structure, and observations other than in 21-cm emission. We show that HVCs contain heavy elements and that the more prominent ones are more than 2 kpc from the Galactic plane. We evaluate the hypotheses proposed for their origin and reject those that account for only one or a few HVCs. At least three different hypotheses are needed: one for the Magellanic Stream and possibly related clouds, one for the Outer Arm Extension, and one (or more) for the other HVCs. We discuss the evidence for the accretion and the fountain model but cannot rule out either one.