The Instatus mobile app gives you push notifications for your monitor alerts, and lets you manage your monitors, incidents, and status pages from your phone.
Open the app and sign in with your Instatus account. Once you're signed in, you'll have access to the same dashboard you use on the web.
During setup, the app asks for permission to send you notifications. Allow it so you can receive alerts on your phone.
Then add Mobile app as an alert channel in your monitor alerts to get notified the moment a monitor fails, degrades, or recovers.