The Huisgen 1,3-dipolar cycloaddition of azides and acetylenes catalyzed by Cu(I) salts, leading to 1,2,3-triazoles, is one of the most versatile "click reactions". We have developed a series of optimized protocols and new applications of this reaction starting from several substrates, comparing heterogeneous vs homogeneous catalysis, conventional heating vs microwave irradiation or simultaneous microwave/ultrasound irradiation. Both non-conventional techniques strongly promoted the cycloaddition (bromide → azide → triazole), that could be conveniently performed in a one-pot procedure. This was feasible even with such bulky molecules as functionalized β-cyclodextrins (β-CD), starting from 61-O-tosyl-β-CD or from heptakis[6-O-(tert-butyldimethylsilyl)]-21-O-propargyl-β-CD. "Greener" heterogeneous catalysis with charcoal-supported Cu(II) or Cu(I) (prepared under ultrasound) was advantageously employed.