The Roman and Byzantine city of Apamea was one of the most prominent of the lost cities of northern Syria, and its ruins were a major archaeological site. As this National Geographic piece (free registration required) notes, satellite photography posted on this Trafficking Culture site shows the archaeological site, pristine in 2011, completely covered with looters' holes in 2012:
Amid fears that ISIS is looting and selling antiquities to finance its conquests, museums have already prepared an Emergency Red List of Syrian Cultural Objects at Risk (PDF) to alert border authorities for possible looted artifacts.
Now the concern is about northern Iraq. By taking Mosul, ISIS also took the ancient site of Nineveh, the Assyrian capital. As Christopher Dickey notes at The Huffington Post, some Iraqi officials are urging the US to use targeted drone strikes to hit ISIS without damaging archaeological sites.
That implies a lot more confidence in Predator accuracy than I'm comfortable with.
Given the scale of human lives lost, many may find the threat to heritage sites a minor one, a sort of "First World Problem." But if one adds to the destruction of sites in Syria and Iraq the looting of museums during the Egyptian Revolution and the Iraq War, the toll over the past decade or so is huge: the past is disappearing.