Vibrations lose energy because of (1) coupling of the system to other systems or to the environment or of (2) intrinsic damping within the system itself. The present paper attempts to survey the current state of understanding for the principal mechanisms of the latter type with explicit physics (rather than purely phenomenological considerations), as simply as practical. Some mechanisms are evidenced in the attenuation of waves in unbounded homogeneous media, others are caused by the presence of boundaries. Some explicitly require quantum-mechanical concepts for their explanation, others can be explained in terms of classical mechanics and thermodynamics. Specific mechanisms that are to be discussed include those associated with thermal conductivity, grain and domain boundary effects, interstitial atom diffusion, relaxation by diffusion, inter-grain diffusion, micro-eddy current losses, hysteresis losses, thermoelastic internal friction, thermal damping associated with transverse vibrations of thin bodies, phonon-phonon interactions, phonon-electron interactions, internal fluids, and dislocations. The concept of relaxation often provides a convenient unified description. Rather than use the local averaged particle displacement as a sole description of the local vibrations, one considers additional local variables, loosely referred to as hidden variables. Each such variable, when disturbed, relaxes to its equilibrium value with a characteristic relaxation time.