Observational data on the appearance and properties of the diffuse interstellar bands (DIBs) are reviewed in the context of a model in which the proposed carriers of these bands are large carbon molecules and carbon nanoparticles containing between 30 and several hundred carbon atoms. The abundance of these carriers, as estimated from the observed strengths of the DIBs, place strong constraints on their rates of formation and destruction, and suggest that the strongest bands, including that at 4428 Å, could be produced via the decomposition of larger carbon particles, possibly those particles that have been postulated to be the source of the 2175 Å extinction feature. Such particles are of mixed sp² and sp³ carbon composition, with sizes between that of large molecules and small macroscopic solids. Any description of their characteristics must combine aspects of molecular and condensed matter physics, and this is incorporated in the present discussion. I discuss recent experimental and theoretical data related to these matters.