You can install our site as a web app on your iOS device by utilizing the Add to Home Screen feature in Safari. Please see this thread for more details on this.
Note: This feature currently requires accessing the site using the built-in Safari browser.
If you have an iPhone, check the App Store for an update for the Tesla app -- now updated to version 3.1.0 as of today. Using the app you can now also monitor your home energy with the Powerwall's Power Flow screen.