MDroid by Exzalt Inc. is the newest mobile app for Moodlers using Android which was derived from the first MDroid by Praveen Kumar Pendyala (free). MDroid by Exzalt is available for a buck from the Google Play store.
I tried authenticating to two sites without success (my own Moodle and Moodle.org). For my own site I was able to login, but no course list was available (my own course site defaults to myMoodle which may have been the culprit), no luck at all at Moodle.org. If you’re feeling adventurous either version (Exzalt’s or Praveen’s) might worth checking out. What is promising and worth noting though is that the app has an offline setting. Once you’re able to establish a connection to a site and have browsed a course, the app will display some of the course resources even in offline mode (which might be a really solid feature for student commuters or teachers looking to peruse course activity even while out of cell/wifi range.
Verdict: shows promise but underwhelms at this time.