The discovery of channels, valleys, and related features of aqueous origin on Mars is of profound importance in comparative planetology. Models of the evolution of planetary surfaces and atmospheres must be reconciled with the diversity, abundance, and origins of channels and valleys on Mars. The term “channel” is properly restricted to those Martian troughs that display at least some evidence of large-scale fluid flow on their floors. Outflow channels show evidence of flows emanating from zones of chaotic terrain. The term “valley” applies to those elongate Martian troughs, or systems of troughs, that also appear to have formed by fluid flow, but which lack a suite of bed forms on their floors. The Martian valleys of greatest interest consist of interconnected, digitate networks that dissect extensive areas of heavily cratered uplands on the planet. The diversity of Martian channels and valleys is nearly as great as that of their terrestrial counterparts. Even though polygenetic and highly modified features abound, water was a necessary ingredient in the various channel- and valley-forming processes. The outflow channels involved large-scale fluid flow, entailing as yet unresolved percentages of liquid and solid phases, entrained sediment, and debris flowage. The formation of valley networks required ground water or ground ice, contributing to sapping and various other hillslope phenomena. Channels and valley networks probably require an ancient epoch with surface temperatures and pressures higher than at present. The aqueous formation of channels is release-limited, requiring short-duration floods of immense volumes. The origin of valley networks is perseverance-limited, requiring the maintenance of prolonged seepage and surface flow. Both phenomena are consistent with a thick, ice-rich Martian permafrost formed either during a volatile-rich early epoch or by very effective recycling of planetary water.