Jailbreak iOS 7.1.X

 

Steps To Jailbreak iOS 7.1 & iOS 7.1.1
 
The installation process of the isn't as simple as the previous jailbreak, but you can follow this Reddit thread: 
Make sure you have iTunes installed.
Edit your iPhone's date to June 2, 2014
Open the PanGu.exe file
Click the black button to the right (also UNCHECK THE CHECKMARK where you see random characters and the "PP")
As soon as the "brush stroke" loading bar fills to 20%, the PanGu app will appear on your phone
Tap it
Select Continue
It will fill the loading brush stroke until 80% and your iTunes will open (it will only open IF you have iTunesHelper.exe on your Windows Taskbar)
Close iTunes
Your device will reboot
When it opens again, wait for the brush stroke to complete to 100%
Your device will reboot once more
The process will be finished 100%
The PanGu app will be replaced with Cydia
Do your usual stuff by opening Cydia and continue with what you want to install by then.
For precautionary measures, install Complete PPSync Remover (on http://cydia.angelxwind.net repo) because even though you uncheck the "PP" on step 4, it installs it anyway (internally without the app showing)

Completable  Devices:This Untethered Jailbreak is compatible with following devices running iOS 7.1-iOS 7.1.1:
iPhone 5s
iPhone 5c
iPhone 4S
iPhone 4
iPad Air
iPad 4
iPad 3
iPad 2
iPad mini
Retina iPad mini
iPod touch 5G