The cartilaginous endoskeleton of chondrichthyan fishes (sharks, rays, and chimaeras) exhibits complex arrangements and morphologies of calcified tissues that vary with age, species, feeding behavior, and location in the body. Understanding of the development, evolutionary history and function of these tissue types has been hampered by the lack of a unifying terminology. In order to facilitate reciprocal illumination between disparate fields with convergent interests, we present levels of organization in which crystal orientation/size delimits three calcification types (areolar, globular, and prismatic) that interact in two distinct skeletal types, vertebral and tessellated cartilage. The tessellated skeleton is composed of small blocks (tesserae) of calcified cartilage (both prismatic and globular) overlying a core of unmineralized cartilage, while vertebral cartilage usually contains all three types of calcification.