Several friends have highly recommended this piece on ISIS in The Atlantic. I haven't finished it yet. It is about 10K words, a very lengthy essay.
For those who don't even want to start it, let me recommend this summary blog post by the Elder of Ziyon. It is lengthy for a blog post, but it's really the equivalent of only a page or two. Some highlights:
[A]s you read it, you see that outside of military annihilation, there is no way to defeat it anyway (although Wood thinks that containment can work over time, causing new recruits to become disillusioned at the failure of the caliphate to continuously expand.)
One major point is that their leaders are not crazy. Their beliefs are consistent and if you are willing to listen to them, they will tell you their strategy and tactics. ...
IS cannot be stopped by religious arguments - because their entire point is to bring Islam back to the 7th century, back to Mohammed's own practices. And any Muslim who argues that Mohammed's methods don't apply nowadays cannot win an argument against IS... [emphasis in the original]...
The author underplays the appeal of a non-hypocritical Islam, when Islam itself has no theological alternative to believing that Mohammed was the perfect prophet and example to mankind. Young people who embrace Islam will be far more likely to choose the strain that is the most internally consistent, and as it stands, that is IS.
In other words, neither arguments nor diplomacy nor military strength will defeat ISIS. It is difficult to pray for world peace under these circumstances, other than as a wonderful dream and hope. To follow this thought, read the Elder's post even if you don't read the more lengthy piece in The Atlantic.