During this decade, a few volcanic eruptions have been recorded under a glacier without breaking through the ice. It has occurred twice under Mýrdalsjökull in South Iceland, both in the year 2000 and 2011. These eruptions are comparatively small and last for a short time. The effect is usually limited to a flood, and in 2000 the bridge over Jökulsá River withstood the extra flow. On the contrary, the flood of 2011 took the bridge over Múlakvísl River.
The floods find their way under a glacier tongue, and this is a picture taken on the middle of Sólheimajökull where the flood of 2000 took place.
On the top, black basaltic sand and volcanic ash covers parts of the ice. The river Jökulsá flows peacefully down below.
The location of those two floods / eruptions are roughly pointed out on this map from Náttúrfræðistofnun of Iceland, with the convection cell grid added.