The chemistry, radiochemistry, radiobiology, and radiopharmacology of radiopharmaceuticals containing copper radionuclides are reviewed. Copper radionuclides offer application in positron emission tomography, targeted radiotherapy, and single photon imaging. The chemistry of copper is relatively simple and well-suited to radiopharmaceutical application. Current radiopharmaceuticals include biomolecules labelled via bifunctional chelators primarily based on cyclic polyaminocarboxylates and polyamines, and pyruvaldehyde-bis(N4-methylthiosemicarbazone) (PTSM) and its analogues. The chemistry of copper, of which only a fraction has yet been exploited, is likely to be applied more fully in the future.