An untethered jailbreak of iOS 8.1.1 and iOS 8.2 beta firmwares has just been released by TaiG. It also works for iOS 8.0 and iOS 8.1.
MuscleNerd confirmed the jailbreak over Twitter; however, he warns that you should probably wait a couple days before attempting.
Looks like TaiG just released a jailbreak for 8.1.1 (and 8.0,8.1,8.2beta). Best to wait a few days just in case
TaiG was part of the controversial iOS 7 jailbreak from the Evad3rs. The jaibreak included the TaiG 'app store' for cracked apps by default in China. Following an outcry from the community the evad3rs responded by updating their jailbreak tool to remove TaiG.