The theory of nuclear electron capture is reviewed in the light of current understanding of weak interactions. Experimental methods and results regarding capture probabilities, capture ratios, and $\frac{\mathrm{EC}}{{\beta }^{+}}$ ratios are summarized. Radiative electron capture is discussed, including both theory and experiment. Atomic wavefunction overlap and electron exchange effects are covered, as are atomic transitions that accompany nuclear electron capture. Tables are provided to assist the reader in determining quantities of interest for specific cases.

DOI:https://doi.org/10.1103/RevModPhys.49.77