The enantioselective version of the Tsuji–Trost reaction is called the Trost asymmetric allylic alkylation (Trost AAA) or simply, asymmetric allylic alkylation (AAA). These reactions are often used in asymmetric synthesis. The reaction was originally developed with a palladium catalyst supported by the Trost ligand, although suitable conditions have greatly expanded since then.
Enantioselectivity can be imparted to the reaction during any of the steps aside from the decomplexation of the palladium from the alkene since the stereocenter is already set at that point. Five main ways have been conceptualized to take advantage of these steps and yield enantioselective reaction conditions. 
These methods of enantiodiscrimination were previously reviewed by Trost:
# Preferential ionization via enantioselective olefin complexation
# Enantiotopic ionization of leaving groups
# Attack at enantiotopic ends of the allyl complex
# Enantioface exchange in the -allyl complex
# Differentiation of prochiral nucleophile faces
The favored method for enantiodiscrimination is largely dependent on the substrate of interest, and in some cases, the enantioselectivity may be influenced by several of these factors.