The satellite systems of Jupiter and Saturn were main targets of the Galileo and the Cassini/Huygens mission. One of the most important findings of the Galileo mission was the detection of induced magnetic fields at Europa, Ganymede and Callisto, regarded as indirect evidence for the existence of subsurface water oceans underneath the icy shells of these satellites. These results are consistent with models of the internal structure and thermal state of the moons. Models of the interior structure of the Saturnian satellites and other icy bodies of the outer solar system suggest the likely existence of subsurface oceans also for some of these objects, including Titan, Triton, Pluto and others. The presence of liquid water layers has important implications not only for astrobiology, but also for the physics of the satellites, e.g., the internal dynamics or the response to tidal forces and the resulting orbital evolution. Focussing on the Jovian and the Saturnian system such consequences are discussed for some of the moons.