Zinc oxide (ZnO) is a metal-oxide semiconductor that has attracted resurgent interest as an electronic material for a range of device applications. In our work, we have focused on how defect properties change as one goes from the bulk to the nanoscale. Infrared (IR) reflectance spectra of as-grown and hydrogen-annealed ZnO nanoparticles were measured at near-normal incidence. The as-grown particles were electrically semi-insulating, and show reflectance spectra characteristic of insulating ionic crystals. Samples annealed in hydrogen showed a significant increase in electrical conductivity and free-carrier absorption. A difference was observed in the reststrahlen line shape of the conductive sample compared to that of the as-grown sample. In addition to hydrogen doping, we successfully doped ZnO nanoparticles with Cu. To probe the electronic transitions of Cu2+ impurities in ZnO nanoparticles, IR transmission spectra were taken at liquid-helium temperatures. Two absorption peaks were observed at energies of 5781 and 5821 cm-1. Finally, we tentatively assign a series of IR spectral lines to Na acceptors.