Recent requirements in the field of non-destructive testing are techniques that quantify micro-structural damage in a wide variety of materials during their manufacture and life cycle for ensuring both their quality and durability. Traditional evaluation techniques such as acoustic pulse echo, impact echo, resonance, ultrasonic transmission, electromagnetic and visual inspection methods are not sufficiently sensitive to the presence and development of domains of incipient and progressive damage. The research presented in this thesis details work undertaken by the author while working at the University of Exeter and is concerned with the development and validation of innovative methods to inspect micro-damage. Various non-linear acoustic measurement techniques, such as detecting defects by measuring the generation of harmonic and inter-modulation products, pulse inversion and resonant frequency deviation has been investigated. In addition to the experimental work new transducers and instrumentation has been developed and used in experimental validation tests on a variety of objects and differing materials. It has been found that the non-linear acoustic testing method provides a practical means by which low levels of progressive damage can be detected and quantified with sensitivities far in excess of that provide by conventional ultrasonic testing methods.