Four basic mechanisms have been proposed to explain the acceleration of winds in late-type stars –– thermal pressure gradients, radiation pressure on circumstellar dust grains, momentum addition by Alfvén waves, and momentum addition by periodic shock waves. In this review I describe recent work in applying these mechanisms to stars, and consider whether these mechanisms can work even in principle and whether they are consistent with recent ultraviolet and X-ray data from the IUE and Einstein spacecraft. Thermally-driven winds are likely important for late-type dwarfs, where the mass loss rates are small, and perhaps also in G giants and supergiants, but they cannot operate alone in the K and M giants and supergiants. Radiatively-driven winds are probably unimportant for all cool stars, even the M supergiants with dusty circumstellar envelopes. In principle, Alfvén waves can accelerate winds to high speeds provided the field lines are initially open or forced open by some mechanism, but detailed calculations are needed. Magnetic reconnection is an interesting suggestion for an acceleration mechanism when the field lines are initially closed. For the Mras and semiregular variable supergiants, periodic shock waves provide a simple way of producing rapid mass loss. Thus we are making some progress in understanding mass loss mechanisms for the cool half of the H-R diagram.