Blizzard's original intention was to open the floodgates and launch the game's open beta this month, but given that we're almost at the end of December and there's still no sign of it, you've probably already guessed that isn't going to happen. This is Blizzard we're talking about, after all, a company famous for not hitting release dates. Or indeed even setting them in most cases.
Instead, the open beta is now set to launch in January of next year, with the extra time being used to ensure the game is stable and ready for the inevitable barrage of new players.
"At BlizzCon, we mentioned that we hoped to get the game into a state where it's ready for open beta this month, but we're just not quite there yet," said production director Jason Chayes in a blog post on Battle.net. "The development team has been working hard to get this out before the end of the year, but our highest priority is that Hearthstone has an awesome launch when all gates are lifted and everyone can download it and play at the same time."
If you already have a Battle.net account, you can still opt-in to the game's closed beta if you do so by January 7. If you had already done so before December 16, you should have received a key by now, so check your spam folder if you haven't seen it yet. If you hadn't, your Battle.net account should be granted access within the first few weeks of January whether or not you claimed a beta key.