One of the key attributes of continuous fiber-reinforced ceramic composites (CFCCs) is their ability to undergo inelastic straining upon mechanical loading. This article reviews the mechanics of inelastic deformation and fracture of CFCCs, as needed for the development of damage-tolerant failure prediction methodologies for use in engineering design. It outlines a general framework for the description of fracture in structural materials in the presence of notches and cracks. The article describes the common classes of fracture behavior of CFCCs and presents the constitutive laws needed to describe crack-tip inelasticity. It demonstrates the effects of inelasticity on crack-tip stress fields and addresses the environmental degradation effects on damage tolerance.