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.