The jailbreak of iOS 7.1 until today it did not exist, as its circulation brought and signaled his death evasi0n7.
The Hacker Winocm announced on Twitter that he managed to create an “iOS 7.1 untethered boot” on an iPhone 4 device.
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The device runs on an A4 chip, which is known to break first with each new one firmware released by Apple. Newer chips are much harder to "untethered boot"
With a short video uploaded to YouTube, Winocm offers us proof that iOS 7.1 is now jailbroken. However, it is probably very difficult to find a "hole" for the other chips. Note that Winocm has never released a jailbreak tool to the public, nor has it ever stated that it will do so at some point in the future.
Watch the video