Christ's instruction in His Sermon on the Mount is exactly what He gave to His servant Moses for Israel. Both teach us that marriage is permanent, its ties so binding that they can be broken only by death—or something worse: physical infidelity, moral abandonment, or sustained abuse by either spouse, all of which Jesus encapsulates in the term porneia, translated as "sexual immorality."
The Pharisees tested our Lord on this point, but His response leaves no doubt on how binding the institution of marriage should be, a standard set from creation:
And He answered and said to them, "Have you not read that He who made them at the beginning 'made them male and female,' and said, 'For this reason a man shall leave his father and mother and be joined to his wife, and the two shall become one flesh'? So then, they are no longer two but one flesh. Therefore what God has joined together, let not man separate." (Matthew 19:4-6)
Because marriage is a creation of God, it possesses a sacredness that no man-devised institution can ever have. This world is trying to exchange the sanctity of marriage for its complete opposite, the profane, but this secular approach will never produce a healthy society.