A full overview on the use of chiral phosphine-olefin ligands 1 in the rhodium-catalyzed asymmetric 1,4-addition of arylboronic acids to alpha,beta-unsaturated carbonyl compounds is described. Effective chiral environment of a Rh/1 complex was shown to resemble that of a Rh/(R,R)-Ph-bod* complex by comparing the experimental results as well as the X-ray crystal structures. High catalytic activity of a Rh/1 complex was disclosed and the catalytic cycle involving a trimer-monomer equilibrium was established through mechanistic studies using a reaction calorimeter and P-31 NMR spectroscopy. A negative nonlinear effect derived from an inactive trimer-active monomer equilibrium of the catalyst was also successfully observed.