What does Romans 16:20 mean?

Paul has been warning the Christians in Rome against false teachers who will come among them and offer a distorted view of Christian truth. He wants the believers to take this warning seriously. He has written that these false teachers do not serve Christ but their own appetites. They are liars looking to deceive naive or innocent Christians.

Now, in offering a hopeful truth, Paul seems to associate these false teachers with the father of lies, Satan himself (Galatians 1:8–9). Paul's final word on the subject seems to be that the God of peace will soon crush Satan under their feet. In other words, the work of Satan among them will ultimately fail and God will prevail through His people.

This verse echoes God's prophetic curse on the serpent in Genesis 3:15, "I will put enmity between you and the woman, and between your offspring and her offspring; he shall bruise your head, and you shall bruise his heel."

This, then, is another reason to be wary of and resist the false teachers. Because they are associated with Satan in deception about the character of God and the gospel, they will ultimately be crushed. Those who follow them will be crushed, as well. Those who remain true to the God of peace, through faith in Christ, will stand forever.

Paul adds a quick blessing to the end of these instructions about false teachers, praying that the grace of Christ would be with them.