Electrochemical and electrocatalytic processes are of key importance for the transition to a sustainable energy supply as well as for a wide variety of other technologically relevant fields. Further development of these processes requires in-depth understanding of the atomic, nano, and micro scale structure of the materials and interfaces in electrochemical devices under reaction conditions. We here provide a comprehensive review of in situ and operando studies by X-ray scattering methods, which are powerful and highly versatile tools to provide such understanding. We discuss the application of X-ray scattering to a wide variety of electrochemical systems, ranging from metal and oxide single crystals to nanoparticles and even full devices. We show how structural data on bulk phases, electrode-electrolyte interfaces, and nanoscale morphology can be obtained and describe recent developments that provide highly local information and insight into the composition and electronic structure. These X-ray scattering studies yield insights into the structure in the double layer potential range as well as into the structural evolution during electrocatalytic processes and phase formation reactions, such as nucleation and growth during electrodeposition and dissolution, the formation of passive films, corrosion processes, and the electrochemical intercalation into battery materials.