This article is concerned with the asymmetric cross-coupling of alkenyl or aryl halides and related compounds with organometallic reagents which is effected by Nickel or Palladium catalysts bearing optically active phosphine ligands, some recent progress in asymmetric cross-coupling catalyzed by Nickel or Palladium compounds are summarized in 37 references in terms of the development of chiral ligands; the effects of structure of catalyst and substrate to product's enantiomeric excess (ee) are reviewed. The possible mechanism of asymmetric induction is also introduced in some examples that have been well studied.

Key words: PALLADIUM COMPOUNDS, NICKEL COMPOUNDS, ARYL HALIDE, HALIDE, CHIRAL REAGENT, CATALYST, ORGANO MAGNESIUM COMPOUNDS, ORGANO ZINC COMPOUNDS, ORGANOMETALLIC COMPOUNDS, CROSSED IMMUNITY, COUPLED