Since their discovery in Voyager images, the origin of the bright polar caps of Ganymede has intrigued investigators. Some models attributed the polar cap formation to thermal migration of water vapor to higher latitudes, while other models implicated plasma bombardment in brightening ice. Only with the arrival of Galileo at Jupiter was it apparent that Ganymede possesses a strong internal magnetic field, which blocks most of the plasma from bombarding the satellite's equatorial region while funneling plasma onto the polar regions. This discovery provides a plausible explanation for the polar caps as related to differences in plasma-induced brightening in the polar and the equatorial regions. In this context, we analyze global color and high resolution images of Ganymede obtained by Galileo, finding a very close correspondence between the observed polar cap boundary and the open/closed field lines boundary obtained from new modeling of the magnetic field environment. This establishes a clear link between plasma bombardment and polar cap brightening. High resolution images show that bright polar terrain is segregated into bright and dark patches, suggesting sputter-induced redistribution and subsequent cold trapping of water molecules. Minor differences between the location of the open/closed field lines boundary and the observed polar cap boundary may be due to interaction of Ganymede with Jupiter's magnetosphere, and our neglect of higher-order terms in modeling Ganymede's internal field. We postulate that leading-trailing brightness differences in Ganymede's low-latitude surface are due to enhanced plasma flux onto the leading hemisphere, rather than darkening of the trailing hemisphere. In contrast to Ganymede, the entire surface of Europa is bombarded by jovian plasma, suggesting that sputter-induced redistribution of water molecules is a viable means of brightening that satellite's surface.