Magma transport pathways through Earth's crust span 12–15 orders of magnitude in time and space, with unsteadiness at all scales. However emergent organization of this system is widespread, recorded by spatial loci of volcanism at the surface and large-scale, rapid outpourings of magma throughout the geologic record. This thesis explores several mechanisms for the organization and time evolution of magma transport, from the deep crust to the surface. A primary focus (Chapters 2–5) is the filling, stability and drainage of magma chambers, structures which function both as reservoirs feeding individual volcanic eruptions and as stalling points in the crust where magma accumulates and differentiation occurs. We show that magma chambers may dictate the spatio-temporal organization of magma rising through crust (Chapters 2–3), control the surface eruptive progression of extreme mantle melting events (Chapter 4), and actively set the size of calderas that form during shallow, crystal rich eruptions (Chapter 5). Each of these chapters explores variations on a hypothesis: interactions between magma chamber stresses and the rheology of surrounding crustal materials evolve during magma transport and this unsteady process helps determine the magnitude, location, and timing of surface eruptions. The last part of this thesis (Chapters 6–7) focuses on surface transport processes, the meandering of melt channels on the surface of glaciers and lava flows. We show that the meandering instability is a generic feature of flow over an erodable substrate, despite significantly different fluid characteristics and erosion mechanics.