There have been a few jailbreaks for iOS 7.1.1, but until now no one other than their creators have been able to use them.
Dubbed “Pangu,” a new untethered iOS 7.1.1 jailbreak has been released by Chinese developers, said to be working on the latest iOS 7.1.1 firmware and supporting all the latest Apple devices, including the iPhone 5 and iPad Air. The people behind it apparently took training from noted jailbreaker i0n1c, and are likely using one of the techniques shown off by i0n1c using an iPhone 5c.
According to iH8sn0w, Pangu installs both Cydia and a Chinese app store with illegal apps, but fortunately contains no malware.
While it can be downloaded now, unfortunately it is currently available (at the below link) for Windows only — meaning that OS X users will have to wait a bit longer, although a Mac version is reportedly coming soon.