This review deals with the asymmetric alkynylation of imines (and iminium ions) to give chiral nonracemic propargylamines. Diastereoselective procedures involved the addition of metal alkynylides to chiral nonracemic imines derived from chiral amines or chiral carbonyl compounds. Enantioselective non-catalytic procedures have been achieved with the use of stoichiometric additives or alkynylboron reagents. Finally, catalytic addition of terminal alkynes or zinc acetylides has been carried out in the presence of chiral metal complexes, especially copper complexes as catalysts.