The famous hacker Stefan Esser aka i0nic published a video on twitter showing the iPhone 5c jailbroken with Cyberelevat0r running on iOS 7.1.1 firmware . Previously i0nic posted a message on Twitter about the current stated that development of untethered jailbreak.
Currently there are no tools available to modify iOS 7.1.1, which is expected on thousands iPhone and iPad. The video below of the iPhone 5c on modified firmware gives hope to the jailbreak community before the release iOS 8. However, i0nic has not confirmed about his intentions on making the jailbreak tool public .
I0n1c previously described in detail how the exploit works using Cyberelevat0r : it uses a vulnerability in the firmware kernel , which is at the level of “normal” OS features . With them you can easily interact even within the iOS “sandbox” .