Web Push notifications with iOS 11.3
Good news -- Apple finally announced that Web Push for iOS is coming in 2023!
Web push notifications: Adds support for opt‑in notifications on iOS. Coming in 2023.
Since this question is tagged with OneSignal, OneSignal has announced that they will also support iOS Web Push once Apple makes it available.
Bad news : Apple has included services worker but not Push API so you can't receive push notification.
https://medium.com/@firt/progressive-web-apps-on-ios-are-here-d00430dee3a7
I'm really disappointed...
EDIT - SEPTEMBER 2019
No improvement about Push notifications on iOS 13.1
EDIT - OCTOBER 2019
You can sign this petition opened by WonderPush.
https://www.change.org/p/tim-cook-apple-inc-implement-web-push-notifications-on-ios-devices
EDIT - MARCH 2020
No improvement about Push notifications on iOS 14
EDIT - SEPTEMBER 2021
No improvement about Push notifications on iOS 15