I was surprised to learn today, via Wikipedia, that the Library of Alexandria may not have been destroyed in a cataclysmic fire as I previously thought but actually encountered a slow and steady decline. However, I see that most of the article linked above is marked as requiring expert opinion and further citations, so I thought I'd ask some experts.

What happened to the Library and its works? Did many end up in the House of Wisdom at Baghdad (as I've also previously heard)? How important was the Library to the Hellenistic world?