Molecular nanoplasmonics exploits collective electron excitations in metal nanostructures to enhance and control properties of molecules under the influence of light. Different theoretical communities contributed to this interdisciplinary research field over the last years, with the aim to interpret and predict the physico-chemical phenomena occurring at the molecular- and nano-scale. In particular, the fast and ultrafast electronic response of the composite system, i.e. molecule+nanostructure, is a key aspect allowing one to understand experimental findings, such as the selectivity in chemical reactions or the enhancement of a specific spectroscopic signal. Time-resolved methods emerged as ideal tools to study the photoinduced plasmon-assisted electron dynamics in molecule+nanostructure systems. In this Chapter we therefore collect the recent advances in the theoretical development for time-resolved quantum-based methods to study electron dynamics in plasmonic systems. Fully quantum and multiscale approaches are reviewed, with different levels of complexity for describing the electronic degrees of freedom. As a perspective for future developments and applications, we then focus on plasmon-induced electron dynamics occurring in photocatalysis and in enhanced circular dichroism of chiral molecules close to nanostructures.
