If you're using a Yubikey device with a Linux computer, you may have noticed that plugging in the device and pressing the button does emit a string of characters, however it fails to work with U2F websites when using, say, Google Chrome. In order to get it working, you'll want to execute the following command and reboot your computer:
sudo sh -c 'curl https://raw.githubusercontent.com/Yubico/libu2f-host/master/70-u2f.rules > /etc/udev/rules.d/70-u2f.rules'
This downloads a file which gives your computer special instructions for handling the Yubikey device. Once that's done and you've rebooted, U2F should work just fine.