Volatiles like H2O and CO2 are only present in the Earth’s mantle at trace concentrations. It is therefore astonishing to note that they exert significant control on igneous processes including melt generation, magma transport, volcanic activity, and magmatic-hydrothermal resource generation. These phenomena fall into the category of multi-phase reactive transports, where solid, liquid, and gas phases interact mechanically and thermodynamically to give rise to complex and nonlinear processes spanning regimes of porous to suspension flows. Process-based computational models offer insights into the inner workings of igneous systems and shed light on the story of magmatic volatiles from source to surface. Here, I will highlight modelling results for two case studies showcasing the role of volatiles as dynamic drivers of volcanic activity. Both studies were conducted with custom-built continuum models combining multi-phase flows of melt, crystals, and bubbles with the thermodynamics of petrological phase relations. The first case study looks at persistently active, open-conduit volcanism and asks the question, what clues surface observations can offer of processes and conditions in the subvolcanic plumbing system. Our models of episodic activity of the lava lake of Mt. Erebus, Antarctica, show that convection driven by the buoyancy of entrained gas bubbles can explain much of the observations. The results support the hypothesis that persistently active conduits remain open because of ongoing bi-directional conduit flow transporting volcanic volatiles to the surface. The second case study investigates the curious tale of the famous iron deposits at El Laco, Chile. Geological observations suggest that the series of massive magnetite ore bodies were emplaced as effusive to mildly explosive products of the volcanic eruption of exotic Fe-rich melts. Combining models of thermodynamic phase equilibria, volcano deformation, and bubbly fracture flow, the riddle of ore generation by volcanic eruption can be unraveled. Our models show that the ore-forming melt is sourced from Fe/Si-liquid immiscibility, concentrated by gravitational separation in a sub-volcanic magma reservoir, and erupted along volcano collapse faults. The surprising results indicate that volatile exsolution upon magma ascent provides enough driving force to erupt an Fe-rich melt almost twice as dense as typical silicate melts. These two studies show how even a little volatiles will go a long way.