Highlights-The review is focused on the mechanistic aspects and recent trends (since 2012) of the metal-catalyzed azide-alkyne cycloaddition (MAAC) so-called "click" reactions with catalysts based on various metals (Cu, Ru, Ag, Au, Ir, Ni, Zn, Ln), although Cu (I) catalysts are still the most used ones.-These MAAC reactions are by far the most common click reactions relevant to the "green chemistry" concept.-Mechanistic investigations are essential to reaction improvements and subsequent applications, and indeed as shown in this review the proposed mechanisms have been multiple during the last decade based on theoretical computations and experimental search of intermediates.-New trends are also presented here often representing both exciting approaches for various applications and new challenges for further mechanistic investigations.

DFT calculations at the PBE0/LANL2DZ level have been performed on model compounds to investigate the reaction mechanism of two recently reported metal-catalyzed alkyne azide cycloaddition (MAAC). The first one, that involves a [Cu(tren)] + Br -catalyst, is shown not to proceed through a metal alkynyl intermediate, but, after precomplexation of the alkyne in an  2 -mode, directly to the 1,4-disubstituted 1,2,3-triazole product, through a metallacyclic transition state. The other system, involving a rare-earth Ln[N(SiMe 3 ) 2 ] 3 complex, is found to proceed through an alkynyl-azide complex which produces an  2 -coordinated heterocyclic ligand before protonation by an incoming alkyne molecule. Our results are discussed with respect to other computational data from the literature.2