The fluorescence and motional dynamics of single diamond nanocrystals in buffer solution and in living cells is investigated. Stable hydrosols of nanodiamonds in buffer solutions are investigated by fluorescence correlation spectroscopy. Measurement of the effective hydrodynamic radius yields particles of 48 nm diameter, which is in excellent agreement with atomic force microscopy measurements made on the same particles. Fluorescence correlation spectroscopy measurements indicate that nanocrystals easily form aggregates when the buffer pH is changed. This tendency is reduced when the surface of the diamonds is covered with surfactants. Upon incubation, cells spontaneously take up nanocrystals that uniformly distribute in cells. Most of the particles get immobilized within a few minutes. The binding of streptavidin to biotinylated aggregates of 4 nm diameter nanodiamonds is demonstrated.