High precision theory of atomic helium

Essentially exact calculations of the nonrelativistic wave functions and energies of helium are reviewed, together with the lowest-order relativistic corrections. The results are extended to the entire singly-excited spectrum of helium by means of asymptotic expansion (core polarization), and quantum defect methods. Comparisons with high-precision experimental atomic transition frequencies then provide a measure of higher-order relativistic and quantum electrodynamic effects. Other applications are discussed, such as the determination of nuclear radii from the isotope shift, and measurement of the fine structure constant from fine structure splittings. Recent progress for the more difficult lithium problem is briefly reviewed.