Volcanic eruptions in the region are known as effusive eruptions, where lava flows steadily out of the ground, as opposed to explosive ones which spew ash clouds high into the sky.
The Krysuvik volcanic system has been inactive for the past 900 years, according to the IMO, while the last eruption on the Reykjanes peninsula dates back almost 800 years, to 1240.
So, in geologic terms, it's been inactive since last Tuesday(?)