What happened with Bitfinex?

So, let me get this straight - what exactly happened with Bitfinex? I've heard some rumors floating around about some serious issues they've been facing, but I'm not entirely sure what the full story is. Could you provide a concise yet informative summary of what went down with this popular cryptocurrency exchange? I'm particularly interested in knowing if their customers were affected, and if so, how? Also, did they manage to recover from this incident, and if so, how did they do it?