The Cu(I)-catalyzed 1,3-dipolar cycloaddition between terminal alkynes and organic azides generating 1,4-disubstituted 1,2,3-triazoles has attracted considerable attention owing to its consistency, specificity, and biocompatibility. Copper nanoparticles supported on various supports such as agarose, cellulose, chitosan, charcoal, activated carbon, silica gel, aminoclay, polymer support like poly(styrene-co-maleimide) (SMI) and polyvinylpyrrolidone (PVP) have been utilized as heterogeneous catalyst for the synthesis of 1,2,3-triazoles. This review summarizes various straightforward and efficient methods for the regioselective synthesis of 1,4-disubstituted 1,2,3-triazoles utilizing supported copper nanoparticles as a source of the heterogeneous catalytic species and water as solvent.