This paper reviews the present state of knowledge about the magnetic fields and the plasma interactions associated with the major satellites of Jupiter and Saturn. As revealed by the data from a number of spacecraft in the two planetary systems, the magnetic properties of the Jovian and Saturnian satellites are extremely diverse. As the only case of a strongly magnetized moon, Ganymede possesses an intrinsic magnetic field that forms a mini-magnetosphere surrounding the moon. Moons that contain interior regions of high electrical conductivity, such as Europa and Callisto, generate induced magnetic fields through electromagnetic induction in response to time-varying external fields. Moons that are non-magnetized also can generate magnetic field perturbations through plasma interactions if they possess substantial neutral sources. Unmagnetized moons that lack significant sources of neutrals act as absorbing obstacles to the ambient plasma flow and appear to generate field perturbations mainly in their wake regions. Because the magnetic field in the vicinity of the moons contains contributions from the inevitable electromagnetic interactions between these satellites and the ubiquitous plasma that flows onto them, our knowledge of the magnetic fields intrinsic to these satellites relies heavily on our understanding of the plasma interactions with them.