Phosphoryl-transfer reactions are central to biology. These reactions also have some of the slowest nonenzymatic rates and thus require enormous rate accelerations from biological catalysts. Despite the central importance of phosphoryl transfer and the fascinating catalytic challenges it presents, substantial confusion persists about the properties of these reactions. This confusion exists despite decades of research on the chemical mechanisms underlying these reactions. Here we review phosphoryl-transfer reactions with the goal of providing the reader with the conceptual and experimental background to understand this body of work, to evaluate new results and proposals, and to apply this understanding to enzymes. We describe likely resolutions to some controversies, while emphasizing the limits of our current approaches and understanding. We apply this understanding to enzyme-catalyzed phosphoryl transfer and provide illustrative examples of how this mechanistic background can guide and deepen our understanding of enzymes and their mechanisms of action. Finally, we present important future challenges for this field.