Propargylamines are an important class of organic compounds that have been widely used as building blocks for the synthesis of various kinds of chemically and biologically relevant compounds. Over the last few years, there have been a rapid growth in the research dedicated to developing the synthetic protocol for propargylamine derivatives. Among various methods that are reported for the synthesis of propargylamines, the three‐component coupling of aldehyde, amine and alkyne (commonly termed as A3 coupling reactions) secured a special place because of its convenient/atom economical approach and thus broadly used by researchers. Our aim in this review is to highlight the most recent advancement on A3 coupling reactions for the synthesis of various propargylamine derivatives as well as on the developments of subsequent transformation of these compounds to useful heterocyclic compounds and the related products.