Winocm has posted a video demonstrating an untethered jailbreak for iOS 7.1, running on what appears to be an iPhone 4 or 4s.
It’s not clear yet if the jailbreak will work for newer devices, or when/if the jailbreak will be made available. As many commenters have pointed out, the demo also does not show Cydia installed on the device.
Older devices like the iPhone 4 are easier to jailbreak, so exploits that work on the iPhone 4 may not work on the newer devices.
No matter what device you have, at this point, you should definitely still avoid updating to 7.1 if you want to keep your jailbreak.