If you're using a stock version of Android (4.3+), then you have access to a list of recent notifications through a settings widget. However, this widget is missing from many of the skinned carrier/manufacturer versions of the mobile OS.
As a solution, Notif Log, an app recently suggested by Android Authority, will keep track of all notifications, even after you've dismissed them. Additionally, this app has a feature to get a reminder for a specific notification when it's more relevant. Here's how to use it:
Step 1: Grab a copy of Notif Log for your Android 4.3+ device.Open the app and grant it access to your notification history (it will prompt you to do so).
Step 2: Open the app and grant it access to your notification history (it will prompt you to do so).
Once notifications start happening, you can open Notif Log to see them in a list.
Step 3: To delete the notifications, swipe them to the right. To snooze them and be reminded later, swipe left and select a preset time or set your own.
Now you won't have to spend time hunting through all of your apps to find out what you missed.