In a surprise tweet this morning team evad3rs announced an untethered jailbreak for all apple devices, including the iPhone 5s and iPad mini, running stock iOS7 and above.
The jailbreak itself can be found at evasion.com with a handy tutorial via @JailbreakMatrix: http://www.jailbreakmatrix.com/tools/evasi0n-for-ios-7-jailbreak-is-out-iphone-5s-ipad-mini
Jailbreaking enables you to run user-created patches and tweaks at the system level, allowing for dramatic changes and improvements to your iDevice – visit JailbreakMatrix’s 100 reasons to jailbreak to see just how awesome this news is:
Cydia is like the App Store for these tweaks, and creator @Saurik quickly responded that he hadn’t had the proper files to update Cydia and the mobile substrate platform, which means for now many of your favourite tweaks will not yet be working.
Here is a list of compatible iOS 7 tweaks (from reddit r/jailbreak):
Update: over-the-air updates to iOS 7 are known to create issues when jailbreaking, be sure to restore/update via iTunes prior to attempted to jailbreak.