Click chemistry is one of the most versatile means for the efficient grafting of larger units such as fluorescence labels or biomolecules onto the surface of nanoparticles. Here, a first study on the applicability of different strategies for the copper-catalyzed azide-alkyne coupling of diamond nanoparticles and organic moieties is reported. Both thermally annealed nanodiamond and mechanically pretreated diamond nanoparticles of different origin can be modified with moieties carrying either azide or alkyne groups. Several organic units have been efficiently "clicked" onto these particles. The method is then applied for the bifunctional surface modification of nanodiamond leading to a material exhibiting carboxylic and alkyne groups at the same time. These can be addressed by orthogonal coupling linkers. A model material carrying two distinct fluorescent dyes is produced this way and shows the characteristic luminescence of both dyes. The findings open the way for the application of nanodiamond as multifunctional labels, drug delivery vehicles, and targeting agents in biomedical applications.