Some asteroids eject dust, unexpectedly producing transient, comet-like comae and tails. First ascribed to the sublimation of near-surface water ice, mass-losing asteroids (also called "main-belt comets") can in fact be driven by a surprising diversity of mechanisms. In this paper, we consider 11 dynamical asteroids losing mass, in nine of which the ejected material is spatially resolved. We address mechanisms for producing mass loss including rotational instability, impact ejection, electrostatic repulsion, radiation pressure sweeping, dehydration stresses, and thermal fracture, in addition to the sublimation of ice. In two objects (133P and 238P) the repetitive nature of the observed activity leaves ice sublimation as the only reasonable explanation, while in a third ((596) Scheila), a recent impact is the cause. Another impact may account for activity in P/2010 A2, but this tiny object can also be explained as having shed mass after reaching rotational instability. Mass loss from (3200) Phaethon is probably due to cracking or dehydration at extreme (∼1000 K) perihelion temperatures, perhaps aided by radiation pressure sweeping. For the other bodies, the mass-loss mechanisms remain unidentified, pending the acquisition of more and better data. While the active asteroid sample size remains small, the evidence for an astonishing diversity of mass-loss processes in these bodies is clear.