Quite Surprisingly, a team of Chinese hackers, Pangu have released an untethered jailbreak for iOS 7.1 and iOS 7.1.1.
This untethered jailbreak is compatible with iPhone 5s, iPhone 5c, iPhone 4S, iPhone 4, iPad Air, iPad 4, iPad 3, iPad 2, iPad mini, Retina iPad mini and iPod touch 5G running iOS 7.1-iOS 7.1.1.
The jailbreak tool is currently available for Windows but works on every iOS
Source: How To Jailbreak iOS 7.1 And 7.1.1 Untethered Using ‘Pangu’ Jailbreak Tool