How will we deal with the ruins should order be restored?

When reading “Ancient City Faces Destruction”, by Dana Ballout in the October 6, 2015 issue of the Wall Street Journal, the latest of the seemingly non-stop reports of the destruction of ancient monuments and sites in the Middle East by Daesh (the preferred name for “Isis”), I began to wonder what will happen conservation wise should a time come when there is stability in the region and governing bodies that are not threatened by the existence of the visible remains of a multiplicity of cultures. Will these destroyed sites be reconstructed in some way either physically or virtually? Or will the ruins be left as is because their destruction is an important part of the history of the sites?