Romans 1:16-4:25 is arguably the first major section of Romans, and it deals with the fact that Christ is the solution God has on offer to the sin problem that all humanity--both Jew and non-Jew--have. Paul begins with the key verses of Romans, which sum up the entire situation (1:16-17). Then he unfolds the coming judgment of God on everyone (1:18-3:20), with no one good enough to escape on the basis of their own goodness, not even the most law-observant Jew. Then he presents God's gracious solution, namely, faith in what God has done through Christ as the only solution (3:21-4:25).
The result is that, "since we have been justified through faith we have peace with God through our Lord Jesus Christ" (5:1). Our trust in what God has done through Jesus--"through whom we have gained access by faith into this grace in which we now stand" (5:2)--has led God to declare us right with him, to "justify" us. We now are at peace with God. We are not facing the wrath of God, "being revealed from heaven against all the godlessness and wickedness" of humanity. "Since we have now been justified by his blood, how much more will we be saved from God's wrath through him!" (5:9).
God did not have to do any of these things. He had no obligation to humanity to fix its problem. What he has done through Christ is rather a demonstration of his righteousness (1:17; 3:25-26). The action of Christ and the action of God are so inextricably intertwined that Paul can move from one to the other without pause. God has demonstrated his love toward us in the fact that while we were ungodly sinners, Christ died for us (5:6-8).
Romans 5-8 then unpack some of the implications of what God has done through Christ. They step-back and unpack the implications of Romans 1-4. The first verses of Romans 5, as you can see above, give a quick summary of our new situation--we have been reconciled to God! The second half of Romans 5 then steps back and puts what Christ has done into a historical perspective.  Christ's act of obedience corresponds to the disobedient act of the first human, Adam. Adam caused the sin problem with his act of sin. Christ solved the sin problem with his act of faith. 
Romans 6 and 7 then step-back and ask about sin and the Jewish Law going forward. If only Christ's death makes a person right with God, then what is the place of the Jewish Law? Why did God institute it in the first place? And if we are not truly judged by the Law, then can we continue sinning just as before, only without any consequences. These chapters can be very confusing, and may indeed have been confusing even to the original audience (cf. 2 Pet. 3:15-16). Paul's answer is that the Law got us ready for Christ and that he actually now enables us to keep its essence, something we ironically were not able to do when we were under the Law.
Romans 8 then triumphantly puts it all together in a climactic celebration of freedom from condemnation, and it looks forward to the final redemption of our bodies and indeed the whole creation. Christ has made us right with God, but we remain in this situation of flesh still. God wants to give life to our mortal bodies even while we are still on earth (Rom. 8:11-13). But we especially look forward to the coming redemption of our bodies and the whole creation when Christ returns (8:22-23). Regardless of current suffering, nothing can compare to what is to come (8:18).
 The biblical authors, as is the case with most of us, did not distinguish strongly between history and the story of the Old Testament. Indeed, some Christians today, called fundamentalists, make it a key item of faith that the stories of the Bible equate exactly with history.
Unfortunately, dogmatism on these sorts of things has rarely made anyone more godly or resulted in greater unity or faith. Rather, it has more often engendered needless argument and unnecessary division. What is worse, it seems to impose foreign expectations on the biblical text that, in the end, result in far more Scripture-twisting in the name of a modern debate, rather than a stance of truly listening to what the biblical texts seem to have been saying.
 See the previous chapter for discussion of the "faith of Jesus Christ."