Someday the world’s liquid fuels needed for ships and airplanes will come from sustainable sources and low-energy processing. We are far from that day. While that fact is unfortunate, it opens up exciting opportunities for researchers from many different fields to work together to realize that vision. I will report on some of my research group’s contributions toward this goal, as we develop and apply quantum mechanics based simulation methods to unravel mechanisms associated with (photo)electrochemical water oxidation and carbon dioxide reduction at semiconductor electrodes. As an example, we believe we have finally identified – after six years of work - the crucial aromatic-amine-derived catalytic intermediate involved in CO₂ reduction to methanol at illuminated compound-semiconductor electrodes. Knowledge of this intermediate lends itself to proposed design principles to enhance the efficiency of this promising photoelectroreduction process.