The transformation was discovered in 1979 by Pierre Crabbé and coworkers at the Université Scientifique et Médicale (currently merged into Université Grenoble Alpes) in Grenoble, France.  As initially discovered, the reaction was a one-carbon homologation reaction (the Crabbé homologation) of a terminal alkyne into a terminal allene using formaldehyde as the carbon source, with diisopropylamine as base and copper(I) bromide as catalyst.
Despite the excellent result for the substrate shown, yields were highly dependent on substrate structure and the scope of the process was narrow.  The author noted that iron salts were completely ineffective, while cupric and cuprous chloride and bromide, as well as silver nitrate provided the desired product, but in lower yield under the standard conditions.
Shengming Ma (麻生明) and coworkers at the Shanghai Institute of Organic Chemistry (SIOC, Chinese Academy of Sciences) investigated the reaction in detail, including clarifying the critical role of the base, and developed conditions that exhibited superior functional-group compatibility and generally resulted in higher yields of the allene.  One of the key changes was the use of dicyclohexylamine as the base.  In another important advance, the Ma group found that the combination of zinc iodide and morpholine allowed aldehydes besides formaldehyde, including benzaldehyde derivatives and a more limited range of aliphatic aldehydes, to be used as coupling partners, furnishing 1,3-disubstituted allenes via an alkyne-aldehyde coupling method of substantial generality and utility.  A separate protocol utilizing copper catalysis and a fine-tuned amine base was later developed to obtain better yields for aliphatic aldehydes.
The Crabbé reaction is applicable to a limited range of ketone substrates for the synthesis of trisubstituted allenes; however, a near stoichiometric quantity (0.8 equiv) of cadmium iodide (CdI) is needed to promote the reaction.  Alternatively, the use of cuprous bromide and zinc iodide sequentially as catalysts is also effective, provided the copper catalyst is filtered before zinc iodide is added.