Recent transport measurements through single molecules are calling upon a detailed theoretical comprehension of quantum transport on the molecular scale. This talk is focused on both general methods and concrete structures. The calculus of linear and nonlinear transport in a molecular device is first addressed by introducing the theoretical tools of coherent transport, density functional and molecular dynamics. The implementation of these instruments to realistic structures allows to draw rather general conclusions on the mechanisms of charge transport in experimental devices. In particular, the analysis of a carbon nanotube ring and a short (polyG-polyC) DNA wire provides physical understanding which is supported by the fairly good agreement with the experimental data. The importance of relying on ab-initio parameter free estimations for catching the finer structure of measurements in most experimental conditions is finally highlighted.