A large body of work to calculate nonrelativistic energies, relativistic co
rrections, and quantum electrodynamic (QED) energy shifts in helium is revi
ewed and compared with experiment. Of particular significance are measureme
nts of the QED (Lamb) shift for the low-lying S-states of helium, where the
accuracy rivals the best measurements in the corresponding He+ hydrogenic
ion. Progress in a program to extract a value for the fine structure consta
nt alpha from a comparison between theory and experiment for the fine struc
ture splittings of the helium 2 P-3(J) manifold of states is discussed. Ext
ensions to three-electron systems such as lithium are briefly summarized.