Photochemistry and molecular photophysics have been highly active fields of research for more than half a century; however, during the last two decades synergistic advances in experimental technology and computational methodology have led to a renewed interest in understanding photochemistry and photophysics at the quantum level - photo-initiated quantum molecular dynamics. One of the grand challenges for the 21st century is to develop such a detailed understanding of energy flow in molecules, following the absorption of a photon, that we can begin to develop the knowledge and tools to control photochemistry. Photo-initiated quantum molecular dynamics is not only core fundamental science, it has potentially wide impact. Perhaps one of the most compelling reasons for developing a more detailed understanding of energy flow in molecules between light, electrons and chemical bonds, is to enable us to contribute to some of the challenges in designing light harvesting systems for clean energy generation thus addressing one of the big problems facing society. There are also important applications in fields such as photocatalysis, the design of efficient light-driven molecular devices for data storage and processing, and photomedicine.