For example, Thucydides, book 3 (Chapter 4, section 1.)
If you look at any academic source of Thucydides, or really any ancient work like this, they will have these numbers making it easy for citing.
Who added these? Sometimes, particularly with old translations, I find that they are not exact, give or take a sentence or two, between differing translations, which makes me think they're quite modern.
But at the same time, they sometimes do not make any sense, coming in the middle of a sentence, which makes me think they may be more established than that.
Anyone have a source or info on how these things generally came to be? And if they were added later how they decided where to place them?
It depends a lot upon the text and how standardised it has become.
For example, Plato's works are usually referenced by Stephanus numbers, using a page and section numbering developed by Henri Estienne dating to 1578. Bekker numbers, similarly for Aristotle texts, date to the 19th century.
In antiquity, though, the only reliable 'division' that is found are "books", so for example Hilary of Poitiers refers to numbered books, and earlier and later books, in his On the Trinity (which is 12 books). The division of a work into 'books' often corresponded to its physical division into scrolls (as most of the texts we're thinking of predate the evolution of the codex).
It's only really in the 4th century AD that 'chapters' become more common. These are sometimes indicated by a kind of reverse-indent, where the first line extends out into the margin. Prior to this, most comments on passages just refer to an author, the work's title, possibly a book, and occasionally a remark like "near the end" or similar. NT texts start to get a kind of numbering system of paragraphs in the 4th century, becoming more common in the 5th, but this does not correspond directly to the chapter system of Langton which only came about in the 13th century.
Most ancient texts, then, with a book/chapter/sentence type division have it because of an editor. This may often be the first critical edition that was published. Some texts end up with different divisions, because a second editor later on decided that the first system of numbering wasn't very good, and they do their own.
That's a rough overview, but in most cases it comes down to the specific text in question.