1,2,3-triazoles are popular heterocycles employed in material sciences and medicinal chemistry as they show antiviral, antibacterial, anti-HIV, antitubercular, and antifungal activities. Triazoles are appealing due to their stability and interesting click chemistry properties. The Cu(I) catalyzed reaction between azides and alkynes affords the 1,4-disubstituted derivative exclusively becoming a useful synthetic tool. However, one of the main drawbacks of the catalyzed reaction is the need to use Cu(I), which is unstable at standard conditions and rapidly oxidizes to the non-active Cu(II). The most common approach when synthesizing 1,4-disubstituted-1,2,3-triazoles is to reduce Cu in situ employing inorganic Cu salts and a reducing agent. The resulting Cu(I) needs to be further stabilized with organic ligands for the reaction to take place. The aim of homogeneous catalysis is to produce a ligand with a dual function both in reducing and stabilizing Cu(I) without interfering in the overall reaction. Instead, heterogenous catalysis offers more options when supporting Cu on nanoparticles, complexes, and composites yielding the desired 1,2,3-triazoles in most cases without the need of a reducing agent under green solvents such as ethanol and water. The catalytic activity of Ag, Ru, and Ce is also discussed. This review exemplifies how the use of homogeneous and heterogeneous catalysts offers new and green methodologies for the synthesis of 1,2,3-triazole derivatives. The materials supporting Cu show catalytic properties like high surface area, acid-base sites or phase transfer catalyst. Although there is no ideal catalyst, Cu remains the most effective metal since it is economical, abundant and readily available.