The modelling of nanoelectronic systems has been the topic of ever increasing activity for nearly two decades. Yet, new questions, challenges and opportunities continue to emerge. In this article we review theoretical and numerical work on two new developments in the theory of molecular-scale electronics. First we review a density functional theory analysis within the Keldysh non-equilibrium Green function formalism to predict nonlinear charge transport properties of nanoelectronic devices. Next we review a recently developed quantum mechanical formalism of current-triggered nuclear dynamics. Finally we combine these theories to describe from first principles the inelastic current and the consequent molecular dynamics in molecular heterojunctions.