In the New Testament, in the Sermon on the Mount, Jesus challenges believers with this: "You have heard that it was said, 'You shall love your neighbor and hate your enemy.' But I say to you, Love your enemies and pray for those who persecute you..." (Matthew 5:43-44). Jesus turns the wisdom of the world upside down. He also provides the ultimate example of this in what he does for the world on the Cross. Through the Cross, Jesus turns his enemies into his friends, because of his love.
But we can also find precursors to Jesus' counter-intuitive enemy-love in the Old Testament. I think specifically here of King David, Jesus' ancestor. Consider King David's relationship with Saul. I have written about that some here. King Saul is filled with jealousy toward David, and over half the book of 1Samuel we see King Saul seeking David's life. The people chant that Saul has killed his thousands... but they also chant that David has killed his ten thousands. This drives Saul to madness. He attempts to kill David on multiple occasions, and he pursues David over miles and various locations. Only through God's providence does David escape with his life.
Saul has effectively made himself to be David's enemy. What else could he have done to make himself more of an enemy?
What happens after Saul dies? David does not automatically become King of all the tribes of Israel. He becomes King of Judah, but Saul's son Ish-bosheth becomes King of Israel. Ish-bosheth was made king "over Gilead and the Ashurites and Jezreel and Ephraim and Benjamin and all Israel." For a number of years there remained strife and war between the tribes of Benjamin and the house of David. In chapter 4 Ish-bosheth is murdered by two captains of his own raiding bands, Rechab and Baanah, stabbed in the stomach. They cut off Ish-bosheth's head and brought his head to David saying, "Here is the head of Ish-bosheth, the son of Saul, your enemy who sought your life." It sounds like they were expecting some praise or reward from David. This was not to be. David reminds them of the fate of the man who brought news of Saul's death - swift justice to the man who laid the sword to the Lord's anointed - and once again David meets the wickedness of these murderers with swift justice. Beyond Saul's death, David continues to treat Saul's descendants with respect and justice.

In King David we see honor. We see goodness. We see loyalty. We see a good example of enemy-love. The love of God is not just a passive love. It is a love that is active, that roams around seeking not to devour as sin would, but seeking ways to do good to people, even to the grandchild of your mortal enemy.
I should not assume that we all take seriously the imperative from Jesus to love our enemies. To some that might sound like an absurdity, and because of that it bounces right off us. But there it remains in all its glorious challenge. When confronted with an impossibility like this, it should lead us to prayer to the God who makes the impossible possible. And I believe a means by which God makes this impossibility possible is through the changing of our hearts. I believe God changes our hearts by lifting up for our admiration Jesus, and those who reflect Jesus well, like David as he related to Saul.