This book introduces the hysteresis and damping of, and damage to, composites. It analyzes the following areas: damage mechanisms affecting the hysteresis of composites, mechanical hysteresis of ceramic-matrix composites, hysteresis behavior of fiber-reinforced ceramic-matrix composites (CMCs), relationship between the internal damage and hysteresis loops of CMCs, and mechanical hysteresis loops and the fiber/matrix interface frictional coefficient of SiC/CAS and C/SiC composites. A damping study on aluminum-multiwalled carbon nanotube-based nanocomposite materials is discussed to increase the damping property for applications like engine heads, pistons, cylinder blocks, and other aerospace components. The effect of ceramic/graphite addition to the dry sliding wear behavior of copper-based hybrid composites has been assessed at three different normal loads of 9.81, 19.62, and 29.34 N. The authors hope this book will help material scientists and engineering designers to understand and master the hysteresis of composites.