Blizzard announced today that the closed beta test of Hearthstone for the European Union folks has begun. The US beta has already been going on for a while, and for the most part, reviews have been positive.
Blizzard also recently ended their US-based Facebook sweepstakes where people had the change to get one of a thousand beta keys. There is no indication yet if such a contest will be offered for the EU side of things. However, keep an eye out -- one has to believe they'll be doing something. If you haven't already you can opt-in to the beta by logging into your Battle.net account and adding Hearthstone to your beta profile. Invites via the opt-in method seem to go out every week or so.
You can catch up on all our latest Hearthstone coverage, and tune in to the podcast every Monday night at 11pm EDT -- we're usually playing it while we talk about WoW.