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.