By standardized, what I mean is that I can reference John 3:16 and that will be recognizable to anyone familiar with the Gospels. But I'm assuming at some point, scholars would have taken the Biblical text and assigned chapters and verses to it.
A couple of other questions related to that:
is the chapter and verse structure assigned to the original languages? I'm assuming that's the case because the verses vary in length; some may be a full sentence while others are just clauses or sentence fragments.
Does the Torah follow the same chapter and verse structure that we'd find in the first books of the Christian bible? Or does it have its own indexing system?
Was this sort of indexing system used for other ancient texts?
The standard divisions typically in use today derive from chapter divisions by Stephen Langton in 1205. He added them to the Latin Vulgate text, and they were only later inserted to corresponding Greek manuscripts in the 15th century.
Robert Estienne in 1551 added verse divisions to his Greek New Testament. These were later expanded to other texts.
Verses generally correspond across languages, though with some variation (psalms texts are often out by a verse because of different systems about whether the header text counts as a verse or not).
Some Byzantine texts have an earlier system of 'chapters' (κεφαλαια), though I'm not super-familiar with them.
The Tanakh had a system similar to, but not identical to, chapter/verse, dating back at least until the Masoretic scribes, marking verses with a pair of dots at the end, kind of like a colon (it's called a silluq). Longer sections are marked by spacings, these involve using a parashah, basically a space before the next section of text, to indicate a section break.
Other ancient texts have varying degrees of indexing. Most ancient books were divided into books/volumes, e.g. the 24 books of the Odyssey, the 12 of the Aeneid. Chapter/section/paragraph divisions were generally added post-antiquity. Some txts have distinct referencing systems in broad usage. For example, Plato is generally references with references to the Stephanus text of 1578.
This may also be a good question to post over in /r/AcademicBiblical as well.