If you use the News app and follow multiple channels, and you have notifications turned on for each of them, you are probably inundated with alerts of breaking news stories. While you likely dismiss most of them, there are probably a few that catch your eye as something worthwhile, but you either don't have time to read them at the moment or aren't in an appropriate setting to do so. If such is the case, you can always save stories to peruse later - a great way to curate a reading list for when you have some down time.
You can clear your Notification Center by deleting each notification individually, or by using 3D Touch to clear them all at once. To individually delete a notification just tap the x above the notification. To clear Notification Center of all notifications at once use 3D Touch to tap and hold the x above any notification, then tap Clear All Notifications.
iOS 11 introduces several changes to notifications on iPhone and iPad including Cover Sheet, which is what the revamped Notification Center is now known as. Cover Sheet looks just like your Lock Screen and shows your notifications in chronological order rather than grouping them by app. While Cover Sheet is still very similar to the old Notification Center, there are noticeable differences in interaction and notification options.
iOS 10 finally gives you the ability to clear all of your notifications out of the Notification Center with one gesture (if you have the iPhone 6s or better). To do it, open your Notification Center by swiping down from the top of your screen, then deep press the "x" close icon to bring up the 3D Touch option to clear all notifications. Tap it and voilà, your notifications are gone.
The jailbreak tweak 3D Touch Notifications offers a new way to interact with iOS notifications from the Notification Center or lock screen. Once installed, peek and pop on the iPhone 6s and 6s Plus can be accessed from the Notification Center just like native 3D Touch. A press will preview the notification contents, and a deep press opens the app.