The efficiency of organocopper reagents in the displacement of allylic leaving groups has been well established during the past five decades. In sharp contrast, catalytic asymmetric version of this reaction using a chiral catalyst is a more recent field of research. This chapter presents an overview of tremendous studies towards the development of an “ideally” active catalyst achieving high regio- and enantioselectivities. The comparative reactivity and generality of peptides, phosphorus, as well as N-heterocyclic carbenes based catalysts are discussed in the first part. Then, relevant scope and synthetic applications are reviewed. Noteworthily, this chapter is restricted to C–C bond formation processes, excluding C–B and C–Si bond formations.