The modification of polymers after the successful achievement of a polymerization process represents an important task in macromolecular science. Cycloaddition reactions, among them the metal catalyzed azide/alkyne 'click' reaction (a variation of the Huisgen 1,3-dipolar cycloaddition reaction between terminal acetylenes and azides) represents an important contribution towards this endeavor. They combine high efficiency (usually above 95%) with a high tolerance of functional groups and solvents, as well as moderate reaction temperatures (25-70 degrees C). The present review assembles recent literature for applications of this reaction in the field of polymer science (linear polymers, dendrimers, gels) as well as the use of this and related reactions for surface modification on carbon nanotubes, fullerenes, and on solid substrates, and includes the authors own publications of references (>100) are included.