A general formalism is developed for the theory of electronic current through a molecule attached to macroscopic electrodes in a given bias. The current is calculated in a non-perturbative many-body formalism. We obtain an intuitively appealing formula. We identify two distinct limits: the Kubo linear response formula valid in the small bias regime and the Landauer formula valid for non-interacting electrons. Finally, we develop a new correlation function formula. which is more amenable to numerical computations and discuss the application of absorbing potentials in the electrodes as a possible means of calculation. (C) 2003 Elsevier Science B.V. All rights reserved.