Hermes: Notification Manager

Hermes was a Greek deity who served as a messenger of the gods using his winged sandles to move freely between the worlds of the mortals and the devine.
The Hermes app, on the other hand, is a service that uses the cloud to move notifications from the world of your Mac to that of your iPhone.
Hermes offers an easy to use API, and a user specific e-mail address that makes it easy to integrate Hermes into whatever automated workflow you might be using.
You don't have to worry about notifications over burdening you with Hermes's forwarding rules. Only forward notifications from the apps you want, and even set up smart rules per app so only the important stuff gets through.
Hermes Terms Of Service: https://funk-isoft.com/tos-hermes.html
Hermes Privacy Policy: https://funk-isoft.com/privacy.html