These verses follow on from those before them. In the Greek there is a connecting word that the NIV translators have left out. And in 17 he tells us that the gospel reveals a righteousness from God that comes by faith. These verses explain why we needed the power of the gospel to give us the righteousness from God that comes through faith. UN-righteous, and under God's wrath.
Wrath is just an old-fashioned word for anger.
And the very first thing we notice here is that God's righteous anger is a present reality. Not just has been revealed, or will be revealed in the future, but is being revealed in this present age. And it is revealed against ALL wickedness. That means not just against Saddam Hussein or mass murderers, but against all who lie, are greedy, selfish, and deny the goodness of God in small as well as big ways. We are all under this umbrella of judgement.