Petrodollars obtained by exporters is used to buy US based assets and/or financial instruments (treasury bonds, stocks, real estate), literally “recycling” all that extra capital... though the Saudis have been dumping a lot of their assets for a few years already, as they plan on diversifying their economy but I guess that’s tangential

A bit late to respond, but I would start with the wikipedia article which is short but gives a decent overview.

https://en.wikipedia.org/wiki/Petrodollar_recycling

The petrodollar warfare section is worthy of note.