Light-matter interactions are fundamentally important in chemistry. While traditional theory usually treats light as an external perturbation on the molecular system, this dissertation emphasizes the significance of self-consistently propagating the coupled dynamics between an electromagnetic field and molecules. The first part of this dissertation focuses on benchmarking conventional semiclassical electrodynamics scheme and extending state-of-art mixed quantum-classical algorithms on modeling fundamental light-matter processes, including spontaneous emission, energy transfer, and collective emission. The second part of this dissertation introduces a novel numerical approach --- classical cavity molecular dynamics (CavMD) --- for simulating vibrational strong light-matter interactions when a large collection of realistic molecules in the condensed phase are confined in an optical cavity. In this vibrational strong coupling regime, CavMD recovers Rabi splitting in the equilibrium infrared (IR) spectroscopy, reveals the mechanism of vibration-polariton (hybrid light-matter state) relaxation and polariton-enhanced molecular nonlinear absorption, and demonstrates the cavity effects on vibrational relaxation and energy transfer in the absence of external polariton pumping --- most of these findings are consistent with experiments. Finally, CavMD also predicts an intriguing energy transfer pathway: by exciting a vibrational polariton of the solvent molecules with an intense IR laser, the input energy may selectively transfer and highly excite the solute molecules; outside the cavity the same pulse fluence can only weakly excite the solute molecules and the selectivity is low. This mechanism, which requires experimental verification, could possibly lead to selective catalysis of ground-state chemical reactions in the condensed phase using an IR laser.