Visible-light-driven photochemistry has continued to attract heightened interest due to its capacity to efficiently harvest solar energy and its potential to solve the global energy crisis. Plasmonic nanostructures boast broadly tunable optical properties coupled with catalytically active surfaces that offer a unique opportunity for solar photochemistry. Resonant optical excitation of surface plasmons produces energetic hot electrons that can be collected to facilitate chemical reactions. This review sums up recent theoretical and experimental approaches for understanding the underlying photophysical processes in hot electron generation and discusses various electron-transfer models on both plasmonic metal nanostructures and plasmonic metal/semiconductor heterostructures. Following that are highlights of recent examples of plasmon-driven hot electron photochemical reactions within the context of both cases. The review concludes with a discussion about the remaining challenges in the field and future opportunities for addressing the low reaction efficiencies in hot-electron-induced photochemistry.