Web Push notifications with iOS 11.3
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
I am following the roadmap of the webkit and it seems they are working on it:
https://webkit.org/status/#?search=manifest
Hopefully by end of the year, It will be released in production.