Ankimote

Ankimote is an addon that adds remote control functionality to Anki, the open source flashcards app.

After installing this addon, selecting 'Ankimote' from the Anki toolbar will start Ankimote and display a QR code and URL directing to the remote that can be accessed by any other device on the local network (usually your phone).

Features

Answer cards (again, hard, good, easy) from the remote and get visual feedback on the desktop app
Scroll up, scroll down, undo from the remote
One-hand (Swipes) and two-hand (Taps) control interfaces
Switch decks without touching your computer
Works with the AMBOSS addon to flip through popups
'Show Hints' action reveals hidden portions of cards in common decks such as Anking and Pepper

Advanced features (see addon config in Anki):

Custom actions to trigger execution of user-defined Python code (to interact with Anki) or Javascript (to interact with the current card)
Custom hook support for integration with other addons

Limitations

Both devices must be on the same network (usually the same WiFi name)
The network must allow local communication (public networks like coffee shops and some schools may not work)
Workaround: when the above conditions cannot be met, try enabling Bluetooth tethering on your phone and connect your computer to your phone's Bluetooth. In your computer's Bluetooth settings, use "connect to network" or similar to create an internet connection over Bluetooth between the two devices. Then find your phone's IP address on the Bluetooth connection, and use that IP address instead of the one Ankimote displays. Use the same port displayed by Ankimote.