The state of knowledge about the structure and composition of icy satellite interiors has been significantly extended by combining direct measurements from spacecraft, laboratory experiments, and theoretical modeling. Interior models of icy bodies will certainly benefit from future missions to the outer solar system, providing new and improved constraints on the surface chemistry, bulk composition and degree of internal differentiation, possible heterogeneities in radial mass distribution, the presence and extent of liquid reservoirs, and the amount of tidal heating for each target body. Here we summarize geophysical constraints on the interior structure and composition of selected Jovian and Saturnian icy satellites and investigate conditions under which potentially habitable liquid water reservoirs could be maintained. Future geophysical exploration which includes gravitational and magnetic field sounding from low-altitude orbit and close flyby, combined with altimetry data and in-situ monitoring of tidally-induced surface distortion and time-variable magnetic fields, would impose important constraints on the interiors of outer planet satellites.