The satellites of the Solar System's giant planets are one of the current frontiers of planetary science, and will be the targets of multiple spacecraft missions in the coming decades. Observations of these objects with ALMA have provided maps of the atmospheres and subsurfaces of these worlds in unprecedented detail, complementing optical/infrared maps of surface composition at a similar resolution. This talk discusses recent ALMA results on Solar System satellites and what we've learned from them about these objects' surface environments, and discusses prospects for discovery with future facilities