The formation, storage and chemical differentiation of magma in the Earth's crust is of fundamental importance in igneous geology and volcanology. Recent data are challenging the high melt fraction 'magma chamber' paradigm that has underpinned models of crustal magmatism for over a century, suggesting instead that magma is normally stored in low melt fraction 'mush reservoirs'. 1-9 A mush reservoir comprises a porous and permeable framework of closely packed crystals with melt present in the pore space. 1,10 However, many common features of crustal magmatism have not yet been explained by either the 'chamber' or 'mush' reservoir concepts. 1,11 Here we show that reactive melt flow is a critical, but hitherto neglected, process in crustal mush reservoirs, occurring because buoyant melt percolates upwards through, and reacts with, the crystals. 10 Reactive melt flow in mush reservoirs produces the low crystallinity, chemically differentiated (silicic) magmas which ascend to form shallower intrusions or erupt to the surface. 11-13 The magmas can host much older crystals, stored at low and even sub-solidus temperatures, consistent with crystal chemistry data. 6-9 Changes in local bulk composition caused by reactive melt flow, rather than significant increases in temperature, produce the rapid increase in melt fraction that remobilizes these cool-or cold-stored crystals. Reactive flow can also produce bimodality in magma compositions sourced from mid-to lower-crustal reservoirs. 14,15 Trace element profiles generated by reactive flow are similar to those observed in a well-studied reservoir now exposed at the surface. 16 We propose that magma storage and differentiation primarily occurs by reactive melt flow in long-lived mush reservoirs, rather than by the commonly invoked process of fractional crystallisation in magma chambers. 14 Magma reservoirs occur at several depths within the crust and typically grow incrementally through the intrusion of dykes or sills. 1,11,13,16,17 High melt fractions must sometimes be present in these reservoirs to produce eruptible, low-crystallinity magmas. 1,7,8,9,13 However, geophysical data suggest that reservoirs have low melt fraction even beneath active volcanoes 2-5 and crystal chemistry data indicate that long-term magma storage occurs at low or even sub-solidus temperature. 6-9 High melt fractions are therefore ephemeral, yet geochemical models typically assume differentiation occurs by crystal fractionation from low-crystallinity magmas; 11,14 moreover, geochronological data demonstrate that crustal magma reservoirs can be long-lived, spanning hundreds of thousands to millions of years. 17-21 Existing models of crustal magma storage and differentiation cannot reconcile these conflicting observations. We use numerical modelling to investigate the storage and chemical differentiation of magma in crustal reservoirs. The model describes repeated intrusion of mafic to intermediate sills into the mid-to lower crust, 12,13,16,21-23 the associated transport of heat via conduction and ad...