We determine the atomic structure of the pseudotetragonal T phase and the pseudorhombohedral R phase in highly strained multiferroic BiFeO(3) thin films by using a combination of atomic-resolution scanning transmission electron microscopy and electron energy-loss spectroscopy. The coordination of the Fe atoms and their displacement relative to the O and Bi positions are assessed by direct imaging. These observations allow us to interpret the electronic structure data derived from electron energy-loss spectroscopy and provide evidence for the giant spontaneous polarization in strained BiFeO(3) thin films.