A growing interest in non-destructive testing methods based on nonlinear acoustics have been observed for the last ten fifteen years. The majority of methods in this area take their origin from the observation that fatigue damaged materials often behave like mesoscopic nonlinear materials (e.g. rocks) in which nonlinear phenomena have been observed for years. The most important phenomena include: higher harmonics generation, vibro-acoustic wave modulations, amplitude dependent resonance frequency shift and slow dynamic effects. All these phenomena result mainly from elastic wave interactions with contact-type defects. There is enough experimental evidence in the literature showing that these nonlinear effects are much more distinct in damaged materials than in intact ones. Despite the fact that many experimental techniques - based on nonlinear acoustic phenomena - have been developed for the last ten years, the physical mechanism of elastic wave interaction with damage materials still not clear. The main reason is the variety of possible nonlinear mechanisms involved. This includes: nonlinear elasticity and dissipation, contact acoustic nonlinearity based on herztian and rough surfaces contact theories and other effects such us adhesion, friction and thermoelasticity. This paper provides a short summary of various theoretical developments and examples of applications to damage detection in different materials.