I have been avoiding poetry in these notes on structure, principally because I am not qualified and secondarily because surely you already know that poetry is structured writing. I will, though, write briefly about one kind of "poetic" structure, because it's one you may not have learned in English 210: chiasmus.
Chiasmus is an ancient literary structure, common in Greek and Latin literature and in both Testaments of the Bible, and it consists of inverted parallelism. In other words, a series of words, ideas, or phrases are repeated, in exactly or nearly exactly reverse order. Scholars analyze chiasms in printed form by further indenting each parallel pair and marking them with coordinating symbols, often a capital letter for the initial series and the same letter with an apostrophe or similar mark for the coordinate in the inverted series.
Here's an example, from Isaiah's commission narrative in the Old Testament (Isaiah 6):
A Make the heart of this people fat,
B and make their ears heavy,
C and shut their eyes;
C' lest they see with their eyes,
B' and hear with their ears,
A' and understand with their heart, and convert, and be healed.
The rhetorical emphasis of a chiasm is often found in its center. In this case, I think the rhetorical point is in the piece of the grammatical unit that sticks out, and doesn't fit the poetic unit. The message that Isaiah is to carry to the people is "convert, and be healed", and the great obstacle is their unwillingness to see, hear and understand.