The latest PS4 Firmware Update has addressed this long-standing oversight, and an app has been released on the App Store to let you take advantage of it.
You will, naturally, need to own the game you are trying to play.
As with the Android and Vita versions, your PS4 needs to be running to allow you to play the games — all the app does is allow your device to act remotely as the screen for your PS4 rather than running the games itself.
This can be any game you’ve downloaded, or one you own physically if the disk is in the drive.
The PS4 Remote Play app is free to download, and your PS4 will install the update allowing it automatically the next time you try and go online if it hasn’t already.
Previously anyone wanting to try and do this would have had to use a third-party app such as R-Play and pay £11.99 for the privilege.