Transition-metal complexes of O2 and N2 play an important role in the environment, chemical industry, and metalloenzymes. This Perspective compares and contrasts the binding modes, reduction levels, and electronic influences on the nature of the bound O2 or N2 group in these complexes. The charge distribution between the metal and the diatomic ligand is variable, and different models for describing the adducts have evolved. In some cases, single resonance structures (e.g. M-superoxide = M–O2−) are accurate descriptions of the adducts. Recent studies have shown that the magnetic coupling in certain N22− complexes differs between resonance forms, and can be used to distinguish experimentally between resonance structures. On the other hand, many O2 and N2 complexes cannot be described well with a simple valence-bond model. Defining the situations where ambiguities occur is a fertile area for continued study.