The new Geeksn0w jailbreak tool finally offers a jailbreak option for iOS 7.1. However, there are a couple of major caveats. First, this is only a tethered jailbreak, meaning the device has to be connected to your computer every time you reboot. Second, the jailbreak only works for A4 devices, like the iPhone 4.
Geeksn0w was released by Black Geek Tutorial (blackgeektuto).