The present disclosure relates to electrolysis systems and methods. The teachings thereof may be embodied in methods and systems for the utilization of carbon dioxide and production of carbon monoxide. For example, a method may include: passing an electrolyte and carbon dioxide in front of a cathode through a cathode chamber; and removing electrolysis byproducts from an electrolyte/electrolysis product mixture using a catalytic filter system. The cathode may include material to reduce carbon dioxide. The process may generate a hydrocarbon compound or carbon monoxide as the electrolysis product and a formate as an electrolysis byproduct. The filter system may include a functionalized complex or a functionalized support material which catalyzes a cleavage reaction of formates (a) to hydrogen and carbon dioxide, or (b) to water and carbon monoxide.