Joe - compound engines, as with any engines, or any engineering if it comes to that, are a matter of efficiency. As I daresay you already know, the vast majority of loco's were simple, not compound; even if they're double-injection, they're still simple, because the steam only works once. For a loco, superheating provided much the same benefits as compounding at lower cost & easier maintenance. Mallets seem to have remained popular into the 50's but aside from them...

Triple-expansion was first used in the SS Aberdeen in 1881 & after that seems to have become fairly standard fairly quickly. There were even quadruple-expansion engines. I can't find a heck of a lot about them, but it seems their principle benefit was more oomph from the same space, so might be used if there was limited space for machinery. The first seems to been installed in a ship called the Suez in 1887. I can only presume they were more expensive to build & maintain, otherwise they would have been more widely used (although it seems P&O used them widely; apparently 80% of their tonnage from 1906-15 was quad-powered!).

And if you're thinking "quintuple?", yes, there were, but they seem not to have been successful. Oddly enough, whilst quad seems to have given more oomph from the same space, the one comment I can find about quin's is that they took up too much space that might otherwise be profitably used for e.g. cargo! And last random fact - apparently all 2,700 Liberty ships built in the US during WWII were triples, because the entirety of steam turbine production was reserved for military ships.

On the subject of pic's, Joe, wiki has multiple pages on steam / compound engines. There's a pretty good shot of a Bavarian compound on their Compound Engine page.