An overview of the many-body problem in atomic and molecular physics and in quantum chemistry is given. Some historical background on the Brillouin-Wigner methodology is presented together with basics derivations of the Rayleigh-Schrödinger and the Brillouin-Wigner perturbation theories. The elementary formulations of the two theories are compared. The recent resurgence of interest in Brillouin-Wigner methodology, particularly in studies of the multi-reference correlation problem, is expalined.