For a long time we've been using and recommending PushBullet as a very convenient way of receiving notifications from astronomy equipment.
We added support for them in the Solo CloudWatcher, and then explained how to send the messages from scripts, so they could be issued from almost all of our products.
Just now, we've added native support in the Dragonfly - in such a way that, even with no PC connected to it, you can get important notifications to your smartphone or PC immediately.
You can, for example, send a message if the roof starts to open while the weather is deemed unsafe. Or if the roof closes while the mount is unparked. First two cases that come to mind...
PushBullet is great, is free for moderate use (although the PRO subscription is worth considering), and no doubt can contribute to being better informed about what's going on at the observatory.