Molecular quantum electrodynamics (QED) is the theory of interaction of molecules with radiation. An essential feature is the application of quantum conditions to the radiation; the associated particles, which are the carriers of the momentum and energy, are photons. In QED the electrodynamic vacuum possesses zero-point energy. Fluctuations in the energy of the vacuum state are the causes of phenomena such as ‘spontaneous’ emission and the Lamb shift, and are the source of the virtual photons important in the understanding of intermolecular interactions. In this connection an attractive feature of the theory is its power to deal with the coupling between molecules within the same framework as radiation-molecule interactions, the molecule-molecule effects being mediated by photons, real and virtual. In this review the multipolar form of QED is described, and applications are given with some emphasis on recent work, for example three-body resonance and synergistic effects in two-photon two-molecule processes. After formulation of the theory, applications are outlined with particular reference to one-and two-photon absorption, spontaneous and stimulated emission, natural and laser-induced circular dichroism, field-induced absorption and harmonic generation. Among intermolecular interactions, accounts are given of resonance and dispersion coupling, molecule-induced circular dichroism, and cooperative two-photon absorption.