Volcanic ocean islands and shield volcanoes form superb natural experiments for investigating changes in topography and hydrology over geologic time. As volcanoes age, their surfaces evolve from un-dissected, highpermeability landscapes into deeply dissected, low-permeability terrain. Here we review the tight links and co-evolution of topographic and hydrologic processes in volcanic landscapes. We discuss a number of factors that affect rates and patterns of hydrological and topographic co-evolution, including soil development, spatial and temporal variability of water availability, flank collapses, geologic architecture, and the tectonic history of subsidence or uplift. To illustrate the effects of climate on volcanic dissection, we compile a global dataset of volcanic landscapes and ages that suggests that substantial dissection begins between 0.5 and 2 million years after construction, with volcanoes in high-precipitation regions tending to become dissected more quickly than those in drier regions. Obtaining a deeper understanding of volcanic landscape evolution will require further research on several topics, such as the sensitivity of river incision to fluctuations in precipitation, the hydrologic responses of soil to chemical weathering and dust deposition, the evolution of chemical and physical erosion rates over a volcano's lifetime, the role of hydrology in triggering of flank collapses, and the extent to which the long-term evolution of an island is determined by the initial and boundary conditions set by geologic structure and regional tectonics.