When a molecule is attached to two metal electrodes with different chemical potentials, the electric current flows through it. The understanding of the fundamental mechanisms of quantum transport in molecule junctions as well as the interpretation of recent experimental molecular conductance measurements require the development of new theoretical/computational approaches to non-equilibrium electronic processes. In my talk, I will discuss theory of the electron transport through molecular contacts. I will present our recent calculations of molecular junctions anchored to gold electrodes by various linkers (dithiocarboxylate, dithiocarbamate) and discuss unusual transport properties we discovered in this systems. I will also give overview of our work on multiscale modeling of molecular STM break junction experiments. If time allows, I will quickly discuss or recent theoretical efforts to perform nonequilibrium electronic structure calculations in Fock-Liouville space.