The fixation of ligands onto molecules, surfaces and materials by use of reactions using a simple and unified chemistry is among the everlasting desires of chemists. Besides the general insensitivity with respect to the chemical structures of the ligand, the completeness of the reaction as well as the insensitivity from external reaction parameters (i.e.: solvents, ambient temperature) is wished. The copper(I)-catalysed azide/alkyne “click”-reaction (also termed Sharpless “click”-reaction, a variation of the Huisgen 1,3-dipolar cycloaddition reaction between terminal acetylenes and azides) is a recent re-discovery of a reaction fulfilling these requirements. Extremely high yields (usually above 95%) are combined with a high tolerance of functional groups and reactions running at moderate temperatures (25°C - 70 °C). The present review assembles recent literature for applications of these reactions in the field of material science, in particular on surfaces, polymers, and for the ligation of ligands to larger biomolecules, including own publications in this field. Since this is an extremely fast developing area, this review offers important knowledge to the interested reader. A number of > 64 references are included.