SQL Server database backup status notification
Backups and Restores should be your Nbr 1 alerts, a failure here can trigger a "CV modification Event". There are several ways to send alerts on a job failure, here you have a screen shot of a job Notifications window. You can use email, pager (do someone still uses this?), net send, write to app log and even delete the job when it finishes (for one time job execution for example).

Email is very common, you just need to notify when the job fails, not every time it succeeds or alike, to avoid unnecessary emails. You will need to enable and setup your Database Mail (if not already done), add an operator (who will receive these emails?), then check Email option and select that operator.

Same with the Alert window, at the end you will end up using an email to notify. This other answer explains this option really well.

But you comment that email is not an option. If you have some kind of monitoring tool for your servers, you can use the Write to Windows Application Event Log and then let that app warn you through whatever means they have configured.