We investigate the depth, variability, and history of regolith on asteroid Vesta using data from the Dawn spacecraft. High-resolution (15-20 m pixel-1) Framing Camera images are used to assess the presence of morphologic indicators of a shallow regolith, including the presence of blocks in crater ejecta, spur-and-gully-type features in crater walls, and the retention of small (<300 m) impact craters. Such features reveal that the broad, regional heterogeneities observed on Vesta in terms of albedo and surface composition extend to the physical properties of the upper 1 km of the surface. Regions of thin regolith are found within the Rheasilvia basin and at equatorial latitudes from 0-90°E and 260-360°E. Craters in these areas that appear to excavate material from beneath the regolith have more diogenitic (Rheasilvia, 0-90°E) and cumulate eucrite (260-360°E) compositions. A region of especially thick regolith, where depths generally exceed 1 km, is found from 100-240°E and corresponds to heavily cratered, low-albedo surface with a basaltic eucrite composition enriched in carbonaceous chondrite material. The presence of a thick regolith in this area supports the idea that this is an ancient terrain that has accumulated a larger component of exogenic debris. We find evidence for the gardening of crater ejecta toward more howarditic compositions, consistent with regolith mixing being the dominant form of "weathering" on Vesta.