My Moodle, formerly the official Moodle Mobile app has been replaced by Moodle Mobile at Moodle.org: http://docs.moodle.org/24/en/Mobile_app. The tool is looking quite polished.
Recently the site was updated with a roadmap for development and additional documentation and screenshots to help highlight the apps advancements. Check out the roadmap at http://docs.moodle.org/24/en/Moodle_Mobile_Roadmap.
The app is free for iOS and Android both
- Android: https://play.google.com/store/apps/details?id=com.moodle.moodlemobile
- iOS: https://itunes.apple.com/es/app/moodle-mobile/id633359593
Below are screenshots of the app as viewed through a tablet: