Released just yesterday, iOS 6.1 can be jailbroken via the program Redsn0w, but only in tethered mode and only for older iDevices.
As detailed by the Microsoft-focused tech site Redmond Pie, Redsn0w version 0.9.15b3 can jailbreak Apple's latest OS. The jailbreak requires that your device be tethered, meaning you'll have to connect it to your computer each time you restart it.
Further, the latest version of Redsn0w supports only older iDevices with an A4 chip or earlier. That means it'll work on devices like the iPhone 4, iPhone 3GS, and 4th-gen iPod Touch but not on the iPhone 5 or the latest iPads or Touches.
However, an untethered jailbreak could kick off as soon as Super Bowl Sunday -- February 3 -- according to Redmond Pie. An iPhone Dev team known as evad3rs has been working on a full iOS 6.1 jailbreak.
The new jailbreak would be untethered, so there'd be no need to connect your iDevice to a PC. And it would support a host of newer devices, including the iPhone 5, the 4th-generation iPad, the iPad Mini, the latest iPod Touch models, and even the latest Apple TVs.
The evad3rs team has set up its own Twitter account and will likely offer up a tweet when the new jailbreak is ready for download.