Many-body approaches to atoms and molecules in external magnetic fields

The proper treatment of many-body effects for fermions has long been a goal of theorists working in atomic and molecular physics. The computational demands of such a treatment however, when coupled to the added difficulties imposed by the presence of external electromagnetic sources, have resulted in few studies of many-body effects in strong magnetic fields, i.e., in the field regime where perturbation theory is no longer applicable. In this article, we review the fundamental aspects of the problem and describe a variety of theoretical approaches for small atoms and molecules in strong fields, beginning with mean-field theory (Hartree-Fock) and progressing through variational and exact stochastic methods.