TaiG

TaiG (Taiji in Chinese) ( /taɪ dʒi/ or /taɪ tʃi/ ) is an untethered jailbreak for all devices on iOS 8.0-8.4, except the Apple TV. It was initially released on 29 November, 2014 for 8.0 - 8.1.2 but since updated to support 8.1.3 - 8.4.

Supported Devices
All devices capable of running iOS 8.0-8.3 (except the Apple TV family) are supported.

iOS 8.2 Beta
TaiG's website originally claimed as early as 4 December 2014 that "support of iOS 8.2 has been completed by TaiG, [but] as 8.2 is still at beta stage, we have disabled support for 8.2 in [the] current public release." This claim remained through 31 December 2014, but was removed sometime before 4 January 2015.

On 23 February 2015, version 1.3 was released to jailbreak iOS 8.2 beta and beta 2.

Installed Packages

 * APR (/usr/lib) (1.3.3-2; )
 * APT 0.7 (apt-key) (0.7.25.3-3; )
 * APT 0.7 Strict (lib) (0.7.25.3-13; )
 * Base Structure (1-4; )
 * Big Boss Icon Set (1.0; )
 * Bourne-Again SHell (4.0.44-15; )
 * bzip2 (1.0.5-7; )
 * Core Utilities (/bin) (8.12-7p; )
 * Cydia Installer (1.1.19; )
 * Cydia Translations (1.1.12; )
 * Darwin Tools (1-4; )
 * Debian Packager (1.14.25-9; )
 * Debian Utilities (3.3.3ubuntu1-1p; )
 * Diff Utilities (2.8.1-6; )
 * Find Utilities (4.2.33-6; )
 * GNU Privacy Guard (1.4.8-4; )
 * grep (2.5.4-3; )
 * gzip (1.6-7; )
 * LZMA Utils (4.32.7-4; )
 * New Curses (5.7-13; )
 * PAM (Apple) (32.1-3; )
 * PAM Modules (36.1-4; )
 * pcre (8.30-5p; )
 * Profile Directory (0-2; )
 * readline (6.0-7; )
 * sed (4.1.5-7; )
 * shell-cmds (118-6; )
 * system-cmds (433.4-12; )
 * TaiG 8.1.3-8.X Untether (2.3.0; )
 * Tape Archive (1.19-8; )
 * UIKit Tools (1.1.10; )

Exploits and analysis
"The Annotated (informal) guide to TaiG - Part I", and "Part II" by Jonathan Levin (iOS 8.0 - 8.1.2)