This mini-review presents a general overview of the progress achieved during the last decade on the amalgamation of CuAAC processes (copper-catalyzed azide-alkyne cycloaddition) with the employment of sustainable solvents as reaction media. In most of the presented examples, the use of water, glycerol (Gly), or deep eutectic solvents (DESs) as non-conventional reaction media allowed not only to recycle the catalytic system (thus reducing the amount of the copper catalyst needed per mole of substrate), but also to achieve higher conversions and selectivities when compared with the reaction promoted in hazardous and volatile organic solvents (VOCs). Moreover, the use of the aforementioned green solvents also permits the improvement of the overall sustainability of the Cu-catalyzed 1,3-dipolar cycloaddition process, thus fulfilling several important principles of green chemistry.