We present a critical discussion of how chemistry textbooks treat the electrolysis of water and aqueous salt solutions, based on a survey of general chemistry textbooks in English and Korean at secondary and tertiary levels, also informed by the historical background of 19th-century debates. English-language textbooks present various and contradictory accounts of the electrolysis of water; a key point of disagreement is whether hydrogen and oxygen gases originate from pre-existing H[superscript +] and OH[superscript -] ions, or from the direct reduction and oxidation of H[subscript 2]O molecules. School textbooks in South Korea all present the same account, with no indication of alternative views. A vast majority of all texts ignore the possibility that H[subscript 2] and O[subscript 2] may result from secondary reactions, which was a standard view in the late 19th century following the works of Daniell and Miller. Concerning the electrolysis of aqueous salt solutions, all texts give oversimplified views of competing reactions based on standard reduction/oxidation potentials. It is understandable that textbooks try to present sufficiently simple pictures that students at each level can handle; however, this should not be done in a way that shuts down questions. We recommend that students should be made aware that textbook accounts are only models, and encouraged to extend their learning beyond the models. The plausibility of our recommendations is shown in a pilot study we conducted with secondary school students in South Korea.