  We present a brief pedagogical review of theoretical Green's function methods
applicable to open quantum systems out of equilibrium in general, and single
molecule junctions in particular. We briefly describe experimental advances in
molecular electronics, then discuss different theoretical approaches. We then
focus on Green's function methods. Two characteristic energy scales governing
the physics are many-body interactions within the junctions, and
molecule-contact coupling. We therefore discuss weak interactions and weak
coupling, as two limits that can be conveniently treated within, respectively,
the standard nonequilibrium Green's function (NEGF) method and its many-body
flavors (pseudoparticle and Hubbard NEGF). We argue that the intermediate
regime, where the two energy scales are comparable, can in many cases be
efficiently treated within the recently introduced superperturbation dual
fermion approach. Finally, we review approaches for going beyond these
analytically accessible limits, as embodied by recent developments in
numerically exact methods based on Green's functions.
