The copper(I)-catalyzed azide􀀀alkyne cycloaddition (CuAAC) reaction is considered to be the most representative ligation process within the context of the 'click chemistry' concept. This CuAAC reaction, which yields compounds containing a 1,2,3-triazole core, has become relevant in the construction of biologically complex systems, bioconjugation strategies, and supramolecular and material sciences. Although many CuAAC reactions are performed under homogenous conditions, heterogenous copper-based catalytic systems are gaining exponential interest, relying on the easy removal, recovery, and reusability of catalytically copper species. The present review covers the most recently developed copper-containing heterogenous solid catalytic systems that use solid inorganic/organic hybrid supports, and which have been used in promoting CuAAC reactions. Due to the demand for 1,2,3-triazoles as non-classical bioisosteres and as framework-based drugs, the CuAAC reaction promoted by solid heterogenous catalysts has greatly improved the recovery and removal of copper species, usually by simple filtration. In so doing, the solving of the toxicity issue regarding copper particles in compounds of biological interest has been achieved. This protocol is also expected to produce a practical chemical process for accessing such compounds on an industrial scale.