Instances of strongly nonadiabatic electronic-vibrational energy transfer have been studied since the early days of quantum mechanics and remain a topic of fundamental interest. Often such transfers are associated with electronic resonances, temporary states where transient localization of charge on the molecule provides a mechanism for channeling electronic energy into vibrational excitation. Extensively studied in the gas phase, electron resonance scattering also occurs with surface adsorbed molecules, where it manifests itself in broadened cross sections and desorption of adsorbates from metal surfaces. In this Account, we focus on a related topic: the implications of nonadiabatic, resonance-mediated scattering to the exciting field of molecular electronics. In this context, researchers can induce directed nuclear dynamics and control these processes in single molecules in contact with metallic and semiconducting electrodes. We discuss a variety of consequences and applications of current-driven nuclear excitation in molecular devices, ranging from the design of new forms of molecular machines to surface chemistry at the single-molecule level and atom-resolved lithography. We highlight two specific examples of molecular nanomachines. In the first, a Au-C(60)-Au transistor, the current induces the oscillatory motion of the center-of-mass coordinate of the C(60). The second, a zwitterion-based rattle, demonstrates excitation of intramolecular motion as the positively charged moiety is threaded back and forth through the negatively charged carbon ring. Finally, we discuss the current-induced desorption of organic molecules from Si(100) both to suggest the potential for controlled surface nanochemistry and to develop guidelines for the design of stable molecular junctions. Modeling the exchange of energy between tunneling electrons and the vibrational degrees of freedom of a target molecule subject to bias voltage, open boundary conditions in the electronic subspace, and the dissipative effects of the electrodes poses a fascinating challenge to contemporary theories of inelastic electron transport. A scattering theory of density matrices is motivated by the need to address large amplitude, chemically relevant dynamics in tandem with an appropriate treatment of the electronic scattering problem. We provide a qualitative discussion of the theory and note the limits in which it reduces to well-known approaches.