The dependence of the damping of Toroidal Alfvén Eigenmodes (TAEs) on various plasma parameters and shapes is analysed with numerical models ranging from perturbative MHD codes like CASTOR-K and NOVA-K, via a warm dielectric tensor model like LEMan to gyrofluid (TAEFL) and linear gyrokinetic codes (LIGKA). Well diagnosed discharges performed in the Joint European Torus (JET) are used to compare theoretical models against experiment. The measurement of TAE damping rates by active in-vessel antennas at JET allows for a direct comparison of both frequency and damping rate with theory.