Now that the dust has settled around Notifications and Stars,
we’ve unleashed all that ✨ in a brand new API. You can now
view and mark notifications as read.

The core notifications functionality is under the /notifications endpoint.
You can look for unread notifications:

$ curl https://api.github.com/notifications

You can filter these notifications to a single Repository:

$ curl https://api.github.com/repos/technoweenie/faraday/notifications

You can read more about this on the API Changes blog, or the full Notifications API documentation.