Solar-powered water splitting with photoelectrochemical (PEC) devices is a promising method to simultaneously harvest and store solar energy at a large scale. Highly efficient small prototype PEC devices reported recently demonstrate a move from basic material research toward design and engineering of complete devices and systems. The increased interest in engineering calls for a better understanding about the operational details of PEC devices at different length scales. The relevant physical phenomena and the properties of typical materials are well-known for separate device components, but their interaction in a complete PEC cell has received less attention. Coupled physical models are useful for studying these interactions and understanding the device operation as a whole and for optimizing the devices. We review the central physical processes in solar-powered water splitting cells and the physical models used in their theoretical simulations. Our focus is in particular on how different physical proce...