Propargylamines are a versatile class of compounds which find broad application in many fields of chemistry. This review aims to describe the different strategies developed so far for the synthesis of propargylamines and their derivatives as well as to highlight their reactivity and use as building blocks in the synthesis of chemically relevant organic compounds. In the first part of the review, the different synthetic approaches to synthesize propargylamines, such as A3 couplings and C-H functionalization of alkynes, have been described and organized on the basis of the catalysts employed in the syntheses. Both racemic and enantioselective approaches have been reported. In the second part, an overview of the transformations of propargylamines into heterocyclic compounds such as pyrroles, pyridines, thiazoles, and oxazoles, as well as other relevant organic derivatives, is presented.