[en] Novel formulations of the two-body bound state problem in quantum field theory are examined. While equal in rigor, these have several calculational advantages over the traditional Bethe-Salpeter formalism. In particular there exist exact solutions of the bound state equations for a Coulomb-like interaction in quantum electrodynamics. The corrections to such zeroth-order solutions can be systematically computed in a simple perturbation theory. These methods are illustrated by computing corrections to the orthopositronium decay rate and to the ground state splittings in positronium and muonium