Newly processed global imaging and topographic mapping of Uranus's five major satellites reveal differences and similarities to mid-sized satellites at Saturn and Pluto. Three modes of internal heat redistribution are recognized. The broad similarity of Miranda's three oval resurfacing zones to those mapped on Enceladus and (subtly) on Dione are likely due to antipodal diapiric upwelling. Conversely, break-up and foundering of crustal blocks accompanied by extensive (cryo)volcanism is the dominant mode on both Charon and Ariel. Titania's fault network finds parallels on Rhea, Dione, Tethys and possibly Oberon. Differences in the geologic style of resurfacing in the satellite systems (e.g. plains on Charon, Dione, Tethys and perhaps Titania versus ridges on Miranda and Ariel) may be driven by differences in ice composition. Surface processes such as volatile transport may also be indicated by bright and dark materials on Oberon, Umbriel and Charon. The more complete and higher quality observations of the Saturnian and Plutonian mid-sized icy satellites by Cassini and New Horizons reveal a wealth of features and phenomena that cannot be perceived in the more limited Voyager coverage of the Uranian satellites, harbingers of many discoveries awaiting us on a return to Uranus.This article is part of a discussion meeting issue ‘Future exploration of ice giant systems'.