The origin and importance of nonlocal damping is discussed through simulations with the generalized nonlocal optical response (GNOR) theory, in conjunction with timedependent density-functional-theory (TDDFT) calculations and equivalent circuit modeling, for some of the most typical plasmonic architectures: metal-dielectric interfaces, metal-dielectric-metal gaps, spherical nanoparticles, and nanoparticle dimers. It is shown that diffusive damping, as introduced by the convective-diffusive GNOR theory, describes well the enhanced losses and plasmon broadening predicted by ab initio calculations in few-nm particles or few-to-sub-nm gaps. Through the evaluation of a local effective dielectric function, it is shown that absorptive losses appear dominantly close to the metal surface, in agreement with TDDFT and the mechanism of Landau damping due to generation of electron-hole pairs near the interface. Diffusive nonlocal theories provide therefore an efficient means to tackle plasmon damping when electron tunneling can be safely disregarded, without the need to resort to more accurate, but time-consuming fully quantum-mechanical studies.