Proof of Concepts
As of April 2016, Proof-of-Concepts have been released, specifically targeting vulnerabilities in the PS4's Internet Browser using the WebKit browser engine.
CVE-2012-3748 (Firmwares < 1.76)
The PS4 Playground by CTurt uses the CVE-2012-3748 WebKit vulnerability.
CVE-2014-1303 (Firmwares < 2.50)
FireKaku (Firmwares <= 3.55 + 3.70(Phat PS4 NOT PRO))
Fire30's proof-of-concept for the WebKit vulnerability used in HENKaku for PSVita 3.60 FW. Support has also been added for 3.15 and 3.50, however the exploit can be ported to all firmwares previous to 3.55.