Stripe's webhooks are really nice. Everything that happens with your account, be it charges, disputes, transfers, or people changing subscription levels, all generate events that you can receive and do something with. In my book and the app that sells it[1] I use them to trigger emails to myself when important things happen. There's also an iPhone app named Paypad[2] that registers a webhook on your account that sends you push notifications when things happen.

[1]: https://www.petekeen.net/mastering-modern-payments

[2]: https://www.pay-pad.com