Ask HN: Notification Management Software?

Does anyone have a good recommendation for a software or service that can receive/handle/organize service notifications?

An example: we have an alert email endpoint that notifications are sent to from our cloud servers. A notification is sent when a service is down, the anti-DDOS software blacklists someone, an API connection fails, someone tries to log in too many times, etc. At the moment, it's just a Gmail inbox and it's messy to say the least.

Is there a dashboard or some service that takes these emails organizes them into a clean dashboard where we can create rules, tags and such to make things easier to manage?