Eruptions beneath ice sheets and glaciers can generate hazardous ash plumes and powerful meltwater floods, as demonstrated by the recent Icelandic eruptions at Eyjafjallajökull in 2010 and at Grímsvötn in 2011. A key scientific objective for volcanologists is to better understand the factors controlling subglacial eruptions, but the eruptions are mostly hidden beneath ice that is often hundreds of metres thick, thereby preventing direct observation. New approaches are therefore needed to reconstruct the factors driving explosive activity and the response of the overlying ice. The dissolved volatile content, preserved in glassy volcanic rock, offers a useful means of reconstructing palaeo-ice thicknesses. However, for subglacial rhyolite at least, there seems to be little or no correlation between loading pressure and eruptive style. Instead, there is a strong correlation between the pre-eruptive volatile content, degassing path and eruptive behaviour. It seems that the style of many subglacial eruptions is controlled by the same mechanisms as subaerial eruptions, with explosivity strongly influenced by degassing and magmatic fragmentation.