Romans 1:18-32 is is part of a section that goes at least to the end of chapter 3. More nearly, the subsection beginning at 1:18 goes to about 2:11. It's hard to find where the seams in the text are, but there are reasons to think that this section doesn’t end with the end of the chapter.

First, prasso, from which we get “practice,” is used in 1:32 ("those who practice these things are worthy of death") and in 2:1-3. In both cases, Paul condemns those who practice what they know to be evil. In 1:32, they practice what they know will be punished with death; in 2:1-3, they do what they condemn others doing.

1:18-32 flows along with two repeated words/phrases move the text along. “Exchange” (allatto or metallatto; 1:23, 25, 26). The first is an exchange of the glory of God for the image of creature, which results in an exchange of the worship of God for the worship of the creature. Then there is exchange of the truth of God for a lie. Finally, an exchange of natural sexual relations for unnatural.

In response, “God gave them over” (1:24, 26, 28), a phrase that marks out three major segments of the passage. These three correspond to the three zones of concern that dominate biblical history: garden/sanctuary, land/home, and outer land/world. Each corresponds to a particular activity in relation to God: The sanctuary is place of worship; the home/land is place of family, sexuality, and interaction with brothers; the world is the place of witness and faithfulness in the face of pressure and persecution. Paul indicts humanity for failing in each area: They don’t honor God (sanctuary); they burn in degraded passion for one another (land); and they commit all sorts of unrighteousness (world).

There’s also a neat structural feature in which Paul gives a brief account of the first sin, with a lengthy description of the consequences of their sin: "They did not honor Him as God or give thanks" is followed by several verses describing the consequences of idolatry (1:21b-25). The same pattern recurs in the last section. “God did not pass the test to have in their minds” is followed by a lengthy description of the consequences (1:28b-32. But the middle example reverses the pattern: a longer description of the sin itself (1:26-27a) is followed by a brief description of the consequences (“receiving in their own persons a due penalty of their error").

It's worth noting that for Paul these evils are not the things that call out the wrath of God, but are the wrath of God taking historical, social, and political forms. The sin that provokes His wrath is at the beginning, but the social chaos at the end, and the sexual confusions of the second stage are manifestations of wrath.

Paul uses a number of rhetorically effective wordplays throughout the section. Idolaters serve "creature" rather than "Creator." Verse 23 contrasts corruptive with incorruptible, a hint of the telos of true and false worship: those who worship corruptible things end in corruption, while those who worship the incorruptible God enter into incorruption. In verse 28, "see fit" and "depraved" share a common root, which has to do with testing the value of metals.

The final list includes 21 different descriptions of human depravity, rising to a crescendo. The Greek phrasing makes it the list even more effective: the first four items in verse 29 are all in the dative, with the same ending, -ia. the last four are all negatives, and begin with the letter “alpha.”