LLM - when did you do yours and why?

Currently finishing off 1L and starting to seriously consider doing an LLM. Most of the lawyers I know have one, and if it could help open more doors or even be able to work in the EU (not necessarily as an attorney) that would be a plus with my dual citizenship. I also just enjoy school. But I'm still a little fuzzy on what exactly an LLM does for you in terms of being more attractive to employers. It looks like there are a lot of different specialized LLM programs so I'm not even sure which ones to look at.

So my question for those attorneys that did their LLM: when did you do it, which one did you do, and why?