Hard, or stony, corals make rocks that can, on geological time scales, lead to the formation of massive reefs in shallow tropical and subtropical seas. In both historical and contemporary oceans, reef-building corals retain information about the marine environment in their skeletons, which is an organic–inorganic composite material. The elemental and isotopic composition of their skeletons is frequently used to reconstruct the environmental history of Earth's oceans over time, including temperature, pH, and salinity. Interpretation of this information requires knowledge of how the organisms formed their skeletons. The basic mechanism of formation of calcium carbonate skeleton in stony corals has been studied for decades. While some researchers consider coral skeletons as mainly passive recorders of ocean conditions, it has become increasingly clear that biological processes play key roles in the biomineralization mechanism. Understanding the role of the animal in living stony coral biomineralization and how it evolved has profound implications for interpreting environmental signatures in fossil corals to understand past ocean conditions. Here we review historical hypotheses and discuss the present understanding of how corals evolved and how their skeletons changed over geological time. We specifically explain how biological processes, particularly those occurring at the subcellular level, critically control the formation of calcium carbonate structures. We examine the different models that address the current debate including the tissue–skeleton interface, skeletal organic matrix, and biomineralization pathways. Finally, we consider how understanding the biological control of coral biomineralization is critical to informing future models of coral vulnerability to inevitable global change, particularly increasing ocean acidification.