Rhodium-catalysed enantioselective hydroboration of olefins is a valuable synthetic transformation, typically employing a chiral catalyst and an achiral borane source. The pertinent chemo-, regio-and enantioselectivity issues of this reaction are discussed. However, the main emphasis of this review is on the evolution of catalytic asymmetric hydroboration. This has primarily relied upon the development and application of chiral bidentate P,P and P,N ligands which have exhibited varying degrees of success in this transformation.