Not getting alert emails

Check spam: look in the junk folder first;
Check recipient verification: System settings → Alert notifications shows Verified / Pending beside each address — unverified ones get no mail; have the recipient click the link in the verification email;
Send a test: click Send test notification to run the whole chain end to end;
Check the inbox: if the notification center has the record but no mail arrived, the alert was generated and the problem is delivery;
Check the retry queue: at the bottom of the settings page — see whether failures are stuck in the queue.

#Still nothing

Switch to your own SMTP Server to rule out platform SMTP being refused;
Check whether global mute was left on;
Consecutive-failure alerts may legitimately be merged or rate-limited by the rules.