Pressure influences both magma production and the failure of magma chambers. Changes in pressure interact with the local tectonic settings and can affect magmatic activity. Present-day reduction in ice load on subglacial volcanoes due to global warming is modifying pressure conditions in magmatic systems. The large pulse in volcanic production at the end of the last glaciation in Iceland suggests a link between unloading and volcanism, and models of that process can help to evaluate future scenarios. A viscoelastic model of glacio-isostatic adjustment that considers melt generation demonstrates how surface unloading may lead to a pulse in magmatic activity. Iceland's ice caps have been thinning since 1890 and glacial rebound at rates exceeding 20 mm yr(-1) is ongoing. Modelling predicts a significant amount of 'additional' magma generation under Iceland due to ice retreat. The unloading also influences stress conditions in shallow magma chambers, modifying their failure conditions in a manner that depends critically on ice retreat, the shape and depth of magma chambers as well as the compressibility of the magma. An annual cycle of land elevation in Iceland, due to seasonal variation of ice mass, indicates an annual modulation of failure conditions in subglacial magma chambers.