Chiral phosphoric acids have become powerful catalysts for the stereocontrolled synthesis of a diverse array of organic compounds. Since the initial report, the development of phosphoric acids as catalysts has been rapid, demonstrating the tremendous generality of this catalyst system and advancing the use of phosphoric acids to catalyze a broad range of asymmetric transformations ranging from Mannich reactions to hydrogenations through complementary modes of activation. These powerful applications have been developed without a clear mechanistic understanding of the reasons for the high level of stereocontrol. This Account describes investigations into the mechanism of the phosphoric acid catalyzed addition of nucleophiles to imines, focusing on binaphthol-based systems. In many cases, the hydroxyl phosphoric acid can form a hydrogen bond to the imine while the P═O interacts with the nucleophile. The single catalyst, therefore, activates both the electrophile and the nucleophile, while holding both in the chiral pocket created by the binaphthol and constrained by substituents at the 3 and 3' positions. Detailed geometric and energetic information about the transition states can be gained from calculations using ONIOM methods that combine the advantages of DFT with some of the speed of force fields. These high-level calculations give a quantitative account of the selectivity in many cases, but require substantial computational resources. A simple qualitative model is a useful complement to this complex quantitative model. We summarize our calculations into a working model that can readily be sketched by hand and used to work out the likely sense of selectivity for each reaction. The steric demands of the different parts of the reactants determine how they fit into the chiral cavity and which of the competing pathways is favored. The preferred pathway can be found by considering the size of the substituents on the nitrogen and carbon atoms of the imine electrophile, and the position of the nucleophilic site on the nucleophile in relation to the hydrogen-bond which holds it in the catalyst active site. We present a guide to defining the pathway in operation allowing the fast and easy prediction of the stereochemical outcome and provide an overview of the breadth of reactions that can be explained by these models including the latest examples.