For iPhone users:
Go back to your main screen
Swipe down from the top of the screen to show "Today" and "Notifications"
Tap on "Notifications"
For Android users:
By creating a shortcut to the notifications section of Settings, you can open up a list of every notification you've received. Here's how:
Open the widget selector.
Find "Settings shortcut" and place it on the screen.
Choose "Notifications" from the menu.
Now, you can tap this shortcut whenever you need to see your old notifications! It won't include everything you've ever gotten since the beginning of time, but it will go back quite a while.