One of the most common reactions I have received to my interpretation of Revelation 20:4-6 is incredulity at the implication that the saints currently reign with Christ in heaven. But this reaction, I believe, is due to an unbiblical understanding of what it means to reign. We tend to think of reigning and serving as two separate and almost opposite things, and yet the very center of Jesus' message in the Gospels is a redefinition of the kingdom into the terms of servanthood (e.g. Mark 10:42-45). To reign means to serve. According to Revelation 5:5-6, it's as the Servant-Lamb that Jesus occupies the throne of God in heaven. And if Jesus reigns right now, then there is also a sense in which we, his people, reign with him through the Spirit — and (I would argue) a further sense in which those who have gone to be with him sit on his throne and reign with him in a new way (e.g. Rev 2:26-27; 3:21).
The opening passage of Revelation says in no uncertain terms that Christ, by his blood, "has made us kings and priests". This is in the past tense. Just as Christ was exalted to the right hand of God where he "reigns," as Paul says, "until he has put all enemies under his feet," so we who are "in Christ" (who are his body, "the fullness of him who fills all in all") reign together through our union with him in baptism. That, I think, is the force of Romans 5:17 in light of the inaugurated eschatology of Romans 6, as it is also a necessary implication of Paul's point in Ephesians 1-2, of our being "seated with Christ in heavenly places".
But how do we "reign" in the present age? This is where a fully-formed biblical theology on the subject is needed, and not just a vague conception based more on the kind of picture which Jesus repudiates in Mark 10:42-45. I can only briefly point us in what I believe to be the right direction.
Then God said, "Let us make man in our image, according to our likeness; let them have dominion over the fish of the sea, over the birds of the air, and over the cattle, over all the earth and over every creeping thing that creeps on the earth." So God created man in His own image; in the image of God He created him; male and female He created them. Then God blessed them, and God said to them, "Be fruitful and multiply; fill the earth and subdue it; have dominion over the fish of the sea, over the birds of the air, and over every living thing that moves on the earth." (Genesis 1:26-28)
From the very beginning humanity was called, as a matter of vocation, to rule over everything that God had made, which means that we were called to reflect, as God's image-bearers, the wise stewardship of the creator outward to his creation. This is a much larger vocation than a "king" (as we think of kings) "reigning" over his kingdom. At most that is a limited metaphor to describe the reality to which we were called. At worst it becomes a gross and beastly parody (as we see clearly in, say, Revelation 13:1-8). But after humanity was expelled from the garden, the place from which we were called to have dominion, God called Abraham to bear his covenant and carry that vocation in a broken and fallen world.
But the question now is this: What does that kingly vocation look like in a context like this, with a largely disjointed and rebellious kingdom? As texts like Exodus 19:6 indicate (and passages like Isaiah 40-55 spell out in detail), the kingdom-vocation which God's people have been called to bear is primarily a servant-shaped and intercessory vocation, a calling to stand as representatives and reflections of God to his creation in outward-focused prayer and mission, and as representatives and reflections of creation (as God intends it to be) back to God in holiness and worship.
And this is exactly the kind of theology which stands behind Revelation's idea of the saints "reigning" with Christ; hence the reason why the role of "kings" is constantly paired with the role "priests". The point is that these are not two separate vocations, but one: we are to be a "kingdom of priests". And it is this priestly kingship which we constantly see in operation throughout Revelation, by the prayers of the saints coming before the throne of God and helping to advance his eschatological plan of redemption (e.g. 5:8; 6:9-11; 8:3-5).
The only difference between the apocalyptic portrait of Revelation and that of (say) Paul, is that whereas Paul's inaugurated eschatology focuses on the "church militant" on earth, John's vision focuses on the "church triumphant" in heaven, i.e. on the souls of the saints reigning with Christ from the heavenly "paradise" by "serv[ing] him day and night in his temple". As Dionysius of Alexandria said of the martyrs in Revelation: "These... who now are assessors of Christ and who share the fellowship of his kingdom, and are partakers of his decisions and judge along with him..." (Letter to Fabius, Eusebius, HE VI.42.5).
There's so much more that could be said, but I must qualify that none of this is meant to imply that we won't ultimately "reign on the earth" in the new creation, as Revelation 5:10 says. We absolutely will. The point, though, is that since Christ really does "reign" at the right hand of God in heaven right now, so all who are "seated with him" reign as well. And if this messes with your definition of what it means to "reign," then that's probably for the best.