Given the practical importance of metallic plutonium, there is considerable interest in understanding its fundamental properties. Plutonium undergoes a 25 per cent increase in volume when transformed from its alpha-phase (which is stable below 400 K) to the delta-phase (stable at around 600 K), an effect that is crucial for issues of long-term storage and disposal. It has long been suspected that this unique property is a consequence of the special location of plutonium in the periodic table, on the border between the light and heavy actinides-here, electron wave-particle duality (or itinerant versus localized behaviour) is important. This situation has resisted previous theoretical treatment. Here we report an electronic structure method, based on dynamical mean-field theory, that enables interpolation between the band-like and atomic-like behaviour of the electron. Our approach enables us to study the phase diagram of plutonium, by providing access to the energetics and one-electron spectra of strongly correlated systems. We explain the origin of the volume expansion between the alpha- and delta-phases, predict the existence of a strong quasiparticle peak near the Fermi level and give a new viewpoint on the physics of plutonium, in which the alpha- and delta-phases are on opposite sides of the interaction-driven localization-delocalization transition.