This thesis describes the study of organozirconium reagents used in copper-catalyzed asymmetric synthesis. Explorations on the asymmetric allylic alkylation of linear substrates, the cyclic substrates and enantioselective desymmetrization of meso compounds including the oxabicyclic alkenes and meso-allyl substrates are reported here. Chapter 1 has a brief overview about general methods used in asymmetric catalysis. In particular, more relevant introduction about catalytic asymmetric allylic substitution and asymmetric desymmetrization of meso compounds is given. Chapter 2 describes the investigation of organozirconium reagents used in copper-catalyzed asymmetric allylic alkylation of linear substrates, and discloses a dynamic kinetic AAA system that employs cyclic allylic chlorides as substrates. Chapter 3 presents the study on expanding the disclosed copper-catalyzed dynamic kinetic AAA chemistry by using more stabilized cyclic allylic phosphate substrates. Further exploration of its possible mechanisms uses substituted substrates, deuterated and enantiopure substrates are also discussed. Chapter 4 demonstrates the study of organozirconium reagents used in copper-catalyzed enantioselective desymmetrization reactions. Investigation of oxabicyclic alkenes and mesoallyl substrates is reported. Chapter 5 gives supporting information of this thesis.