Looks like everything is back up and running.
Updating the PlayStation Network Status Page at 12:40pm PT/3:40pm ET, Sony has confirmed that the PSN is down on PlayStation 4:
Gaming & Social (PS4)
You may have some difficulty launching games, applications, or online features. Our engineers are working to resolve the issue as soon as possible, and we thank you for your patience.
Issues seem to go back a couple of hours ago, with the PS4 version of Call of Duty: Black Ops 3 at Defcon 2, saying, “Online services are degraded. Users in some regions may experience connectivity issues.” Treyarch then added, “We are aware of the connectivity issues on the PS4. We are investigating and will keep you posted. Thank you for your patience.”
Update: Treyarch now says, “Connectivity restored to the PS4. Groups functionality will be temporarily disabled for troubleshooting purposes. We’ll keep you posted.”
Have you been experiencing any problems with the PSN today?
PSN Down on PS4, Black Ops 3 Multiplayer Experiencing Connectivity Issues