Proceeding their 7.50 PS4 OFW today Sony pushed live yet another PS4 System Software / Firmware 7.51 stability update... making the PlayStation 4 the most stable video game console to date! 
As always DON'T UPDATE if you wish to use PS4 game backups and homebrew apps when a new PS4 jailbreak exploit such as TheFloW's FW 6.20 Kxploit arrives, and we'll add any related Tweets below as PlayStation 4 scene developers have a chance to examine it.
Download: PS4 Firmware 7.51 Update (US) / PS4 Firmware 7.51 Update (EU) / PS4 Firmware 7.51 Update (UK) / PS4 Firmware 7.51 Update (AU/NZ) / PS4 Firmware 7.51 Update (JP)
Here's the official 7.51 PS4 Firmware Changelog from Sony's page:
About PlayStation 4 system software version 7.51
Main features in version 7.51 update
Here are some guides for those new on How to Block PS4 Firmware Updates, How to Delete Downloaded PS4 Update PUPs that haven't been installed yet, How to Update to a Specific PS4 Firmware and also some PS4 HEN Update Blocker Payloads.
Spoiler: Related Tweets

Download: PS4 Firmware 7.51 Update (US) / PS4 Firmware 7.51 Update (EU) / PS4 Firmware 7.51 Update (UK) / PS4 Firmware 7.51 Update (AU/NZ) / PS4 Firmware 7.51 Update (JP)
Here's the official 7.51 PS4 Firmware Changelog from Sony's page:
About PlayStation 4 system software version 7.51
Main features in version 7.51 update
- This system software update improves system performance.

Spoiler: Related Tweets