Ubuntu 14.04 and 16.04+
Ondřej Surý provides a PPA for installing PHP 7.0 and 7.1. The latest release can be installed using these commands:
sudo add-apt-repository ppa:ondrej/php
sudo apt-get update
sudo apt-get install php7.0
(Replace 7.0 with 7.1 if desired)
The full list of available packages can be found here: https://launchpad.net/~ondrej/+archive/ubuntu/php/+packages?field.name_filter=php7.0