The app tray takes on a new look.
Those two buttons you see suggest actions you often do. It's meant to be a time-saving feature.
Swipe right on the new home button to scroll through your open apps, one by one.
New volume controls include a slider.
This shows a notched bottom in addition to a notched top. It's there for developers to make sure apps work with this setup.
You can see the new home button on the bottom of the page.
Search results now include richer information, little "slices" of an app that you may or may not have downloaded. For example, search Lyft and you'll be able to see how much a ride home costs.
Selecting text gives you the ability to act on the information right away.
Here's the start screen of Android P on the demo device I used, with no notch set up.
The quick access shade also gets a refresh.
You can manage your notifications.
Turn the phone and a new button will appear to ask if you'd like to rotate the screen.
The back button appears when you can actually go back to another page. Otherwise, you won't see it.
The home screen loses the Back and Recents buttons. Press and hold the home button for Google Assistant.
Notifications get a new look in Android P.
Long-press the power button to turn off the phone or even trigger a screenshot.