Review of high precision theory and experiment for helium

Progress in obtaining essentially exact solutions to the nonrelativistic Schroedinger equation for the entire singly-excited spectrum of helium and other three-body systems is reviewed, and a new upper bound for the ground state is presented. The calculation of relativistic and quantum electrodynamic corrections is discussed, including high precision values for the Bethe logarithm. The results are compared with high precision measurements of ionization energies in helium. Recent progress is reviewed in determining the fine structure intervals in helium with the objective of determining the fine structure constant to an accuracy of ±1.7 parts in 108 or better. Extensions to lithium-like systems are briefly summarized