The phosphoric acid catalyzed reaction of 1,4-dihydropyridines with N-arylimines has been investigated by using density functional theory. We first considered the reaction of acetophenone PMP-imine (PMP=p-methoxyphenyl) with the dimethyl Hantzsch ester catalyzed by diphenyl phosphate. Our study showed that, in agreement with what has previously been postulated for other reactions, diphenyl phosphate acts as a Lewis base/Brønsted acid bifunctional catalyst in this transformation, simultaneously activating both reaction partners. The calculations also showed that the hydride transfer transition states for the E and Z isomers of the iminium ion have comparable energies. This observation turned out to be crucial to the understanding of the enantioselectivity of the process. Our results indicate that when using a chiral 3,3'-disubstituted biaryl phosphoric acid, hydride transfer to the Re face of the (Z)-iminium is energetically more favorable and is responsible for the enantioselectivity, whereas the corresponding transition states for nucleophilic attack on the two faces of the (E)-iminium are virtually degenerate. Moreover, model calculations predict the reversal in enantioselectivity observed in the hydrogenation of 2-arylquinolines, which during the catalytic cycle are converted into (E)-iminium ions that lack the flexibility of those derived from acyclic N-arylimines. In this respect, the conformational rigidity of the dihydroquinolinium cation imposes an unfavorable binding geometry on the transition state for hydride transfer on the Re face and is therefore responsible for the high enantioselectivity.