With increasing advances on nanotechnology, the nanostructured copper catalysts have attracted much attention in alkyne-azide click reaction in the last few years owing to their large surface area, tunable morphology and sustainable catalytic activities. Supported copper nanoparticles are most widely employed. The shape, size and dispersity of supported copper nanoparticles are highly controlled by the used supports, as these will determine the catalytic activity of the heterogeneous click reaction. On the other hand, nanoporous coppers with specific three-dimensional open pore network structure was reported most recently, which can be fabricated with a tunable ligament or pore size without any supports, exhibiting high catalytic activity and reusability. This Minireview describes the state of the art with respect to the fabrication and catalytic application of both supported copper nanoparticles and nanoporous copper in click reaction.