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Detonation nanodiamonds (DNDs) have unique physical and chemical properties that make them invaluable in many applications. However, DNDs are generally assumed to show weak fluorescence, if any, unless chemically modified with organic molecules. We demonstrate that detonation nanodiamonds exhibit significant and excitation-wavelength-dependent fluorescence from the visible to the near-infrared spectral region above 800 nm, even without the engraftment of organic molecules to their surfaces. We show that this fluorescence depends on the surface functionality of the DND particles. The investigated functionalized DNDs, produced from the same purified DND as well as the as-received polyfunctional starting material, are hydrogen, hydroxyl, carboxyl, ethylenediamine, and octadecylamine-terminated. All DNDs are investigated in solution and on a silicon wafer substrate and compared to fluorescent high-pressure high-temperature nanodiamonds. The brightest fluorescence is observed from octadecylamine-functionalized particles and is more than 100 times brighter than the least fluorescent particles, carboxylated DNDs. The majority of photons emitted by all particle types likely originates from non-diamond carbon. However, we locally find bright and photostable fluorescence from nitrogen-vacancy centers in diamond in hydrogenated, hydroxylated, and carboxylated detonation nanodiamonds. Our results contribute to understanding the effects of surface chemistry on the fluorescence of DNDs and enable the exploration of the fluorescent properties of DNDs for applications in theranostics as nontoxic fluorescent labels, sensors, nanoscale tracers, and many others where chemically stable and brightly fluorescent nanoparticles with tailorable surface chemistry are needed.