Reformed thinkers commonly say that Christians will rule with God, particularly Christ, over all the new creation. Wayne Grudem references this passage and simply says:
We shall also have positions of rule over God's entire creation.
Anthony A. Hoekema draws parallels to the early chapters of Genesis, in which Adam and Eve are given dominion over creation, and to the promise of the inheritance of land given to Abraham, arguing that the New Earth will be the ultimate fulfillment of these promises for God's people. He concludes:
This will be a reigning over the new creation. Man will now be able to fulfill in a perfect way the mandate to have dominion over the earth which he could only fulfill imperfectly on the present earth. In the life to come, in other words, man will for the first time since the fall rule the earth properly.
John Frame argues similarly, and specifically mentions several ways Christians will exercise authority:
We are to reign with Christ. That includes judging angels (1 Cor. 6:3), judging Israel (Matt. 19:28; Luke 22:30), ruling cities (Luke 19:11–27). God gave to Adam and Eve authority to have dominion over the earth. Now the saints of Christ receive the authority that Adam forfeited by his sin.
Frame also suggests that the parable of the minas (Luke 19:11–27) may indicate varying degrees of authority among the saints in heaven, though such inequality, he argues, would not lead to unhappiness or jealousy.
- Frame, Systematic Theology, 1081
- Grudem, Systematic Theology, 1163–64
- Hoekema, The Bible and the Future, 283