The volcano warning level has been raised to red, the highest, and the area's already been evacuated.
Deep underground a sharp increase in volcanic activity has been recorded over recent days.
It is a reason for concern after ash from an eruption of another Icelandic volcano in 2010 shut down much of Europe's airspace for six days. Ten million travellers were affected.
It's uncertain that the eruption will stay below the glacier so these scientists are closely examining seismic activity.
There's a significant risk that this eruption could also emit ash clouds.
If that happens, flights could be rerouted or even grounded and with the holiday season in full swing, that's not good news for travellers.
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