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.