How do I see old notifications?

Well that *****. Hopefully Apple will realize this is a mistake.

Notifications are generated by developer‘s apps themselves, or come from their own companies servers. They are inherently transient information. Apple doesn’t control app notifications and they do not originate from Apple - the developers of third party apps control and generate their own notifications. Apple is nothing more then the equivalent of the US postal service - they deliver the notification but they do not generate it, store it, archive it nor own it.

https://developer.apple.com/notifications/

A mistake? Then how are you supposed to dismiss notifications? Do you want last year's notifications still on your phone? Once you acknowledge them, they are gone. If you wish check your Notification settings, you can see if there is something there that you like.

Once you dismiss a notification, there is no way to see it again, except to go to the app in question and see if there are changes, such as a message received in Messages, etc.