If you are not receiving notifications on your Apple Watch, make sure that the iPhone connected to your watch is configured as a device in your user profile.
In order to receive SMS notifications, you'll need to be able to receive short code messages (contact your carrier for assistance with short code messages). Please see Troubleshooting Notifications Issues for more info.
If you are not receiving push notifications, our Apple Push Notification Troubleshooting Guide has more info.
Your watch must be on your wrist to receive notifications.
Your iPhone must be locked to receive watch notifications.
On your iPhone, notifications must be turned ON for both the PagerDuty app AND the Apple Watch app.
You can find this under Settings → Notifications → PagerDuty → Allow Notifications.