It has long been known that the Dirac‐Coulomb Hamiltonian HDC, often used in the past as the basis for relativistic calculations of the spectra of heavy atoms, has no bound states. A review is given of a QED‐based approach to this problem. It yields a configuration‐space Hamiltonian H+, which is protected from the troubles of HDC by the appearance of positive‐energy projection operators surrounding the electron‐electron interaction. Several choices for H+ are considered and compared. The relation between the Dirac‐Hartree‐Fock type equations obtained from HDC and H+ is discussed. Applications to concrete physical problems which have been made with H+‐type hamiltonians are described.