Ice retreat on volcanoes reduces pressure at the surface of the Earth and induces stress changes in magmatic systems. The consequences can include increased generation of magma at depth, increased magma capture in the crust, and modification of failure conditions of magma chambers. We review the methodology to evaluate each of these effects, and consider the influence of ongoing ice retreat on volcanoes at the Mid-Atlantic divergent plate boundary in Iceland. Evaluation of each of these effects requires a series of assumptions regarding the rheology of the crust and mantle, and the nature of magmatic systems, contributing to relatively large uncertainty in response of a magmatic system to climate warming and associated ice retreat. Pressure release melting due to ice cap retreat in Iceland may at present times generate a similar amount of magma as plate tectonic processes; larger than realized previously. However, new modelling shows that part of this magma may be captured in the crust, rather than being erupted. Gradual retreat of ice caps do steadily modify failure conditions at magma chambers, which is highly dependent on their geometry and depth, as well as the details of ice load variations. A model is presented where long-term ice retreat at Katla volcano decreases the likelihood of eruption, as more magma is needed in the magma chamber to cause failure than in the absence of the ice retreat.