As of 6.50 PlayStation 4 firmware update, streaming has been made possible between your PS4 console and the newly-released PS4 Remote Play app.
It was possible for the owners of PS4 to remote play their games on iOS devices for a couple of years now, but only via some third-party applications that you had to buy on the app store. Now, with the official PS4 Remote Play app, players can do the same without spending any money.
There are few limitations with the functionality: you’ll need an iPhone 7 or at least sixth-generation iPad to use it, and it is also available over Wi-Fi only. Other than that, the only thing players have to do is to download the app, pair it with their PS4 over the network, and start games that are compatible using the on-screen buttons.