The ultraviolet and optical telescope (UVOT) on Swift provides coverage of gamma-ray bursts and their afterglows in the 170-650 nm band, yielding multiwavelength data of considerable diagnostic power in conjunction with the Swift X-ray Telescope. The results from the first eighteen months of operation show a broad range of afterglow behaviour, with considerably more complexity in many bursts than would be expected from the simple fireball model for the explosion. We briefly illustrate the capabilities of UVOT for measuring the evolution of nearby supernovae by reference to the observations of GRB 060218, and discuss the peculiar case of GRB 060614, which apparently resides in a nearby galaxy but which did not show the expected supernova feature in its light curve due to radioactive nickel decay. We discuss how the combination of X-ray and UV/optical spectral data can be used to investigate the environment of GRB host galaxies.