What reionized the Universe, and when?

When did the Universe first become transparent? 

It’s a weird question, but an important one. The Universe started off opaque, but became transparent some time after, and remains that way even today. It’s literally why we can see distant objects in the sky, and in a more existential sense that moment of cosmic transparency affected how galaxies behaved, how stars formed, and more. We’re here because of it, and it has profound implications for objects we like to study, so answering the question ...