The linear destabilization and nonlinear saturation of energetic-particle driven Alfvenic instabilities in tokamaks strongly depend on the damping channels. In this work, the collisionless damping mechanisms of Alfvenic modes are investigated within a gyrokinetic framework, by means of global simulations with the particle-in-cell code ORB5, and compared with the eigenvalue code LIGKA and reduced models. In particular, the continuum damping and the Landau damping (of ions and electrons) are considered. The electron Landau damping is found to be dominant on the ion Landau damping for experimentally relevant cases. As an application, the linear and nonlinear dynamics of toroidicity induced Alfven eigenmodes and energetic-particle driven modes in ASDEX Upgrade is investigated theoretically and compared with experimental measurements.