Apple released the new iOS 8.4.1 just 2 days ago. and it seems users should be happy staying with jailbroken iOS 8.4.0 yet since Apple announced that all security bugs that TaiG had exploited are fixed completely now in 8.4.1.

Jailbreak iOS 8.4.1

Apple has just fixed the 8 security bugs related to TaiG tool:
CVE-2015-5746 : evad3rs, TaiG Jailbreak Team
CVE-2015-5766 : TaiG Jailbreak Team
CVE-2015-5752 : TaiG Jailbreak Team
CVE-2015-3806 : TaiG Jailbreak Team
CVE-2015-3803 : TaiG Jailbreak Team
CVE-2015-3802 : TaiG Jailbreak Team
CVE-2015-3805 : TaiG Jailbreak Team
CVE-2015-5774 : TaiG Jailbreak Team

The problems are just technology and time. TaiG or other teams will release their solutions shortly, and we can jailbreak iOS 8.4.1 very soon. We are going to keep updating this topic constantly.

Therefore, it sounds funny there is still a way to jailbreak iOS 8.4.1:

Downgrading iOS 8.4.1 to iOS 8.4 > Jailbreak iOS 8.4 quickly in seconds with TaiG.