A theory that has gained popularity lately is that "put away" and "send away" in key passages don't actually describe a full, legal divorce.
Quick Critiques
A common doctrine in Christianity is that Yeshua only allowed divorce for adultery and that the Torah allowed divorce for any reason.
The words "house" and "youth" are key to understanding what is being addressed and what is simply left to be deduced.
Romans 13:1 Let every soul be subject unto the higher powers. For there is no power but of God: the powers that be are ordained of God.
What happens to an unfaithful wife according to the Torah? Mapping it out in a chart helps show that only one option ends with divorce as all the others are already covered by other punishments.
This is written in response to the following comment I received in an online discussion.
The Bible gives us a few instructions for all marriage.
I have read several places recently that Paul must have been referencing Greek or Roman civil law, not God's law or the Old Testament.