Tidal interactions play a key role in the dynamics and evolution of icy worlds. The intense tectonic activity of Europa and the eruption activity on Enceladus are clear examples of the manifestation of tidal deformation and associated dissipation. While tidal heating has long been recognized as a major driver in the activity of these icy worlds, the mechanism controlling how tidal forces deform the different internal layers and produce heat by tidal friction still remains poorly constrained. As tidal forcing varies with orbital characteristics (distance to the central planet, eccentricity, obliquity), the contribution of tidal heating to the internal heat budget can strongly change over geological timescales. In some circumstances, the tidally-produced heat can result in internal melting and surface activity taking various forms. Even in the absence of significant heat production, tidal deformation can be used to probe the interior structure, the tidal response of icy moons being strongly sensitive to their hydrosphere structure. In the present paper, we review the methods to compute tidal deformation and dissipation in the different layers composing icy worlds. After summarizing the main principle of tidal deformation and the different rheological models used to model visco-elastic tidal response, we describe the dissipation processes expected in rock-dominated cores, subsurface oceans and icy shells and highlight the potential effects of tidal heating in terms of thermal evolution and activity. We finally anticipate how data collected by future missions to Jupiter's and Saturn's moons could be used to constrain their tidal response and the consequences for past and present activities.