The prescriptions used today in celestial mechanics to describe dynamical processes, such as tidal interactions, are somewhat crude. In particular, the quality factor Q, quantifying the tidal dissipation, is often taken as constant, despite its dependence on internal structure, and thus on the tidal frequency. In a solid layer, Efroimsky & Lainey (2007) showed the importance of using a realistic prescription of Q to estimate the evolution speed of the Mars-Phobos system. Such studies confirm the necessity to go beyond evolution models using ad-hoc Q values. Recent astrometric observations of the dynamical evolution of the Jovian and Saturnian systems have shown a higher tidal dissipation than expected (for Jupiter: Q≈3.6×10^4, and for Saturn: Q≈1.7×10^3, from Lainey et al. 2009,2012 resp.). According to a recent model of the Saturnian system formation, such a high tidal dissipation is required by the satellites to migrate up to their present location over the age of the solar system (Charnoz et al., 2011). Globally, gas giants are constituted by a large fluid envelope and a dense central icy/rocky core (Hubbard & Marley 1989). Fluid models, where the tide excites the inertial waves of the convective envelope, show that the resulting tidal dissipation is of the order of Q≈10^5-10^7 (Wu 2005, Ogilvie & Lin 2004). These models have neglected the possible dissipation by the core. Thus, we have developed a model evaluating the tidal dissipation in the anelastic central region of a two-layer planet, surrounded by a static envelope, tidally excited by the hostingstar or a satellite (Remus et al., 2012). The tide exerted by the companion deforms both the envelope and the core. Because of its anelasticity, the core also creates tidal dissipation. I will discuss how the tidal dissipation depends on the rheological parameters and the size of the core. Assuming realistic models of internal structure and taking into account the frequency dependence of the solid dissipation, I will show how this mechanism might compete with the dissipation in fluid layers, and even explain the observed values of tidal dissipation. [abridged]