Methods for covalently modifying surfaces of various substrates are disclosed, along with various substrates having surfaces modified by such methods. Candidate surfaces include various polymeric, siliceous, metallic, allotrophic forms of carbon, and semiconductor surfaces. The surfaces are exposed to a reagent, having molecules each comprising a nitrenogenic group and a functionalizing group, in the presence of energized charged particles such as electrons and ions, photons, or heat, which transform the nitrenogenic reagent to a nitrene intermediate. The nitrene covalently reacts with any of various chemical groups present on the substrate surface, thereby effecting nitrene addition of the functionalizing groups to the substrate surface. The functionalizing groups can then participate in downstream chemistry whereby any of a large variety of functional groups, including biological molecules, can be covalently bonded to the surface, thereby dramatically altering the chemical behavior of the surface. Such functionalizations of the surface can be done in a single reactive step or in multiple reactive steps.