EDIT: Added another relevent video.
Recent talks from Google I/O 2016:
Service Workers - Instant Loading: Building offline-first Progressive Web Apps
A good potion of this walks through the “offline” capability.
Web Push Notifications
A walk though what push notifications should be used for, overview of systems involved and basic code patterns.
Note the recent name change from “Google Cloud Messaging” (GCM) to “Firebase Cloud Messaging” (FCM).
These videos are long, the first is 45 minutes long so - do yourself a favour and use the Video Speed Controller extension in Chrome.