In recent years, advanced composite materials have been frequently selected for aerospace applications due to their light weight and high strength. Polymer matrix composite (PMC) materials have also been increasingly considered for use in elevated temperature applications, such as supersonic vehicle airframes and propulsion system components. A new generation of high glass-transition temperature polymers has enabled this development to materialise. Clearly, there is a requirement to better understand the mechanical behaviour of this class of composite materials in order to achieve widespread acceptance in practical applications. This book presents and discusses the results and apparent shortcomings in studies of levels of fatigue in polymer matrix composites.