Sharks, rays and other elasmobranch fishes are characterized by a skeletal type that is unique among living vertebrates, comprised predominantly of an unmineralized cartilage, covered by a thin outer layer of sub-millimeter, mineralized tiles called tesserae. The mineralized portion of the skeleton appears to grow only by apposition, adding material at the edges of each tessera; maintenance of non-mineralized joints between tesserae is therefore vital, with precise control of mineral deposition and inhibition at the many thousands of growth fronts in the skeleton. Yet, we have only scattered evidence as to how the elasmobranchs mineralize and grow their skeletons. In this review, we take an “environment to skeleton” approach, drawing together research from a vast range of perspectives to track calcium and phosphate from the typical elasmobranch habitats into and through the body, to their deposition at tesseral growth fronts. In the process, we discuss the available evidence for skeletal resorption capability, mineral homeostasis hormones, and nucleation inhibition mechanisms. We also outline relevant theories in crystal nucleation and typical errors in measurements of serum calcium and phosphate in the study of vertebrate biology. We assemble research that suggests consensus in some concepts in elasmobranch skeletal development, but also highlight the very large gaps in our knowledge, particularly in regards to endocrine functional networks and biomineralization mechanisms. In this way, we lay out frameworks for future directions in the study of elasmobranch skeletal biology with stronger and more comparative links to research in other disciplines and into other taxa.