Understanding current flow through molecular conductors involves simulating the contact surface physics, the molecular chemistry, the device electrostatics, and the quantum kinetics of nonequilibrium transport, along with more sophisticated processes such as scattering and many-body effects.We summarize our current theoretical understanding of transport through such nanoscale devices. Our approach is based on self-consistently combining the nonequilibrium Green's function (NEGF) formulation of transport with an electronic structure calculation of the molecule.We identify the essential ingredients that go into such a simulation. While experimental data for many of the inputs required for quantitative simulation are still evolving, the general framework laid down in this treatment should still be applicable.We use these concepts to examine a few prototype molecular devices, such as wires, transistors, and resonant-tunneling diodes.