Romans 8 begins with the words, "Now, because of this,". So you have to ask "Because of what?" The apostle Paul is continuing his thoughts from the previous chapter, where he spoke of the conflict we have with our new nature that has been made possible because of God's grace and the fallen nature of our flesh; the chapter ended with the words, "I thank God I can be free through Jesus Christ our Lord!"
And so because of this, and I'm now quoting the rest of the opening sentence of chapter 8 "… those who belong to Christ will not suffer the punishment of sin." Or as the KJV puts it "There is therefore now no condemnation to them which are in Christ Jesus, who walk not after the flesh, but after the Spirit."
Think of it! Paul just got done saying that the things he does not want to do he does, and the things he does want to do he does not do. So in other words, he still sins! But because of what Jesus accomplished with his death on the cross and subsequent resurrection, we who are his will not suffer the punishment of sin! Why? Because he took our sins upon himself and paid the price. And so, righteousness is accounted to us. And the entire chapter elaborates on this beautiful and awesome truth.