Nonequilibrium processes involving electronic and vibrational degrees of freedom in nanoscale materials are under active experimental investigation. Corresponding theoretical studies are much scarcer. The review starts with the basics of time-dependent density functional theory, recent developments in nonadiabatic molecular dynamics, and the fusion of the two techniques. Ab initio simulations of this kind allow us to directly mimic a great variety of time-resolved experiments performed with pump-probe laser spectroscopies. The focus is on the ultrafast photoinduced charge and exciton dynamics at interfaces formed by two complementary materials. We consider purely inorganic materials, inorganic-organic hybrids, and all organic interfaces, involving bulk semiconductors, metallic and semiconducting nanoclusters, graphene, carbon nanotubes, fullerenes, polymers, molecular crystals, molecules, and solvent. The detailed atomistic insights available from time-domain ab initio studies provide a unique description and a comprehensive understanding of the competition between electron transfer, thermal relaxation, energy transfer, and charge recombination processes. These advances now make it possible to directly guide the development of organic and hybrid solar cells, as well as photocatalytic, electronic, spintronic, and other devices relying on complex interfacial dynamics.


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