In the first part, a review is made of the development of the many-body perturbation theory for the last half century. The development of methods for quantum electrodynamics (QED) calculations, which have occurred essentially in parallel, is also briefly reviewed. In the second part, an effort of unifying the two is discussed. The covariant-evolution-operator method, developed primarily for QED calculations by the Gothenburg group, can be combined with atomic/molecular many-body perturbation theory (MBPT) and for the first time making it possible to combine full QED with electron correlation of arbitrary order. The basic idea is to extend the standard procedure of MBPT to a time- or energy-dependent formalism, which makes it possible to include QED perturbations in a rigorous fashion. The procedure has been implemented and as a first test applied to helium like ions. The method can also be applied to dynamical processes. © 2014 Wiley Periodicals, Inc.