Scholarship in antiquity

I know I have at least a few people reading this journal who know a bit about this topic. 🙂

Scholars in the ancient world: what exactly did they do? What sorts of things did they write? “Commentaries,” according to the references in the things I’ve read, but what exactly was the content and purpose of those things? What other kinds of works did they produce?

What sparked this question was thinking about the Library of Alexandria and the scholars who used it, but I’m also interested in answers from other parts of the world (since the purpose to which I’d be putting this is not historical fiction). Ancient Confucian scholarship, ancient Vedic scholarship, those and more would all be interesting to know about, too.