The topography of volcanic arcs reflects a combination of magmatic ascent processes that deform the overlying crust, volcanic eruptions that blanket the surface in lava and ash, and geomorphic processes that shape these deposits into the observable landscape and consequently record an erosional archive of surface deformation. A central goal of geomorphology is to utilize the form of landscapes to infer the processes that shape them, yet comparatively little work has been done to quantitatively understand the geomorphology of volcanic landscapes. The Central Volcanic Zone of the South American Andes (CVZ, 15-28°S) represents an ideal location for understanding the processes that shape the surface of volcanic arcs; the arid climate and well-constrained geochronology of volcanic deposits provide a geomorphic archive going back 11 Myrs, and the wealth of available geophysical imaging data provides a high-resolution glimpse into the subsurface. In this thesis I utilize geormophic and geophysical data to explore fundamental questions in volcanic landscape evolution at varying spatial scales. To begin, I examine the isostatic uplift response to crustal intrusion of mantle-derived melt, resulting in growth of the largest known active magma reservoir on Earth (the Altiplano-Puna Magma Body). From topography I show that it is possible to calculate the contribution of mantle-derived melt to crustal thickening, and I compare these results to independent seismic estimates that agree well with our data. I then use the record of volcanic deposits from the Altiplano-Puna Magma Body to estimate the flux of mantle melt into the crust, and show that predicted uplift rates are comparable to the surface uplift associated with convective lithospheric removal. Next, I explore how the topography of individual volcanic systems can help discern the style of melt ascent from deeper crustal magma reservoirs to shallow ones. Using two actively deforming volcanoes in the CVZ, Uturuncu volcano and the Lazufre volcanic complex, I use river profiles, lake shorelines, and lava flow deflections to infer each volcano's surface deformation record into the geomorphic past. Uturuncu volcano shows little signs of permanent paleo-deformation, suggesting transient ascent of magma over millenial timescales, while Lazufre's long wavelength deformation suggests continued accumulation of magma since > 0.3 Ma. Finally, I utilize the unique topography of a windswept ignimbrite erupted from the Altiplano-Puna Magma body to better understand how wind abrasion can incise bedrock canyons, a fundamental geomorphic process in arid landscapes on both Earth and Mars. Using a natural experiment within the 4 Ma Puripicar ignimbrite on the western slope of the Central Andes, we quantify the relative contribution of wind and water erosion in propagating bedrock canyons and show that wind can incise canyons an order of magnitude faster than rivers, streamlining their profiles in the process. Thus, in these chapters I illustrate how geomorphology can be a useful tool for quantifying subsurface magmatic processes, while volcanic landscapes themselves can also provide unique opportunities for understanding fundamental planetary geomorphic processes not often observed elsewhere on Earth.