Romans 12:17-19 meaning

Paul's message is relentlessly consistent: we should not put ourselves in the place of God. Be humble, live in reality, do not be haughty. See ourselves and the world around us as it really is. Do not curse enemies. 

Paul continues in this same vein, exhorting believers who seek to live a life with a renewed mind that is apart from that of the world: to not take vengeance on anyone for anything, never pay back evil for evil to anyone (v 17). Never take your own revenge, but leave room for the wrath of God (v 19); it is His role to deal out judgment toward wickedness. 

We are not God, so we shouldn't try to avenge ourselves; instead, we should get out of God's way. Respect what is right in the sight of all men. If possible, so far as it depends on you, be at peace with all men (vv 17-18). 

Paul was quite harsh on those who slandered his message (Romans 3:8), but never sought vengeance himself (Romans 3:9). He leaves that to God. He recognizes that all have sinned, including him (Romans 3:10-11). 

In verse 19, Paul quotes Deuteronomy 32:35, where God makes clear to Israel that all deeds will be brought to justice: 'Vengeance is mine, I will repay' says the Lord (v 19). 

God will take care of all wrongs, and it is important that we not try to do God's job for Him. In fact, if we try to do God's job for Him, we might be getting in the way of justice being done.

It is worth noting that this quote from Deuteronomy is in the context of God judging Israel for disobedience, but also judging Israel's enemies for abusing them. The next verse is God assuring Israel that He will deliver them:

"For the LORD will vindicate His people,
And will have compassion on His servants."
(Deuteronomy 32:36a)

The LORD is the judge of all and will judge with perfect judgement. When we judge others we establish a standard by which God will judge us (Matthew 7:1-2). 

Have peace with all men, Paul writes, if it's possible. It isn't always possible because we do not make choices for others. But as much as we can manage, we are to be peaceful with other people, Christian or otherwise. 

We can control what we do, not what others do. Even if someone is committed to opposing us at every turn, we have the choice not to retaliate. The idea of peace is harmony of the community. So a major way we can pursue this is to pursue goals that actually benefit the community. When there are those who seek evil and harm upon the community, then we are to oppose them, perhaps through the agency of government (Romans 13:3). 

It is important to remember that Paul is writing to a church body. We can avoid falling into petty conflicts if we live humbly with one another (v 16), not arrogantly. We can remain in reality and avoid trying to be the judge and jury if we let God be God and recognize that He'll be the one to right all wrongs. By following God's ways, we will avoid trying to dominate others for the sake of our sinful pride. The result of living with such love and service toward one another is communal harmony around a shared purpose of elevating one another. The Bible calls such a lifestyle "righteousness." 

God's will is that we live righteously (meaning living rightly, justly, and correctly—as God designed life to be, which is harmonious living). Living harmoniously is not consistent with being arrogant or thinking we are better than others. Since we are all equal in value, there is no basis for judging others—we can choose not to take our own revenge. Rather, we can leave room for the wrath of God. We can trust that God will bring all things to justice, and believe what He has said: for it is written, "Vengeance is Mine, I will repay," says the Lord.

When we look at God as the Judge and the King, and we look at one another as people to serve rather than control, our faith is in God, not ourselves. Living righteously is only accomplished by faith, as the theme verse of Romans says: 

"For in it the righteousness of God is revealed from faith to faith; as it is written, 'But the righteous man shall live by faith.'"
(Romans 1:17)

Paul is expressing transformative principles, not a to-do list. He began this chapter by speaking of being transformed by having a new way of thinking. He is teaching attitudes rather than rules to follow. 

If we follow the Spirit and live the way Paul is describing, we will continue to be transformed to the image of Christ. When called to serve other believers, we are to do so emphasizing our gifts, by meeting people where they are and seeking their best.