If you have been eagerly waiting to jailbreak iOS 8, it might become a possibility after the final release of iOS 8.4. Apple patched up all the security exploits that were used by TaiG with the release of iOS 8.1.3 and since then we haven't seen any solution and workaround to the problem. However, iOS 8.4 final release is expected to bring some new developments in the jailbreaking community.
Jailbreak iOS 8.4 expected in June:
We did see i0n1c sharing a proof of concept jailbreak iOS 8.4 video which he achieved on beta 1 of the latest iOS. However, do not expect to see the jailbreaking solution coming to you before the final release of iOS 8.4.
Industry analysts claim that iOS 8.4 will be the final update before iOS 9 is released at WWDC. This actually means that Apple stops caring about iOS 8 and starts focusing on patching things up with iOS 9 giving some much-needed hope to the users who have been looking forward to a JB solution.
With Apple widely expected to unveil iOS 9 at the WWDC, and follow it up by releasing it to developers, it does look like iOS 8.4 will be the final version for iOS 8. In case of iOS 7 last year, iOS 7.1.2 was the final release, so Apple has already released a lot more software updates for iOS 8. It also seems unlikely that Apple will waste any more resources on iOS 8, as Apple Engineers will be busy fixing the bugs in iOS 9 to be able to get ready for the release in September... - iPhonehacks
i0n1c's video confirms that iOS 8.4 jailbreak is very much possible and under works, however, no one would risk releasing it now and getting exploits patched up in the final release. Apple's iOS 8.4 final public release is expected this month or in June.
Currently, it seems like jailbreaking community is playing a silent game waiting for Apple to move its cards. Once the final iOS 8.4 public release is seeded out, it is expected that we will see either the iOS 8.3 or the iOS 8.4 jailbreak solution depending on the security level of upcoming OS.
In the meantime, work on your temptation of jailbreaking your iOS and stay clear of any sites that claim to give you jailbreaks for iOS 8.1.3 up as all of them are scam.