The Official Moodle Mobile apps have come a long way since Moodle4iPhone and the
latest next release will enable PUSH notifications for your app. Two pre-reqs help make it happen: your Moodle site must be registered with Moodle.org and you must be able to install a message plugin/addon.
Users still will need to select which types of messages can be pushed to their phones, but it should be an awesome way to allow students to get updates on messages, grades, etc. from their cell phone or tablets. Check out the docs at http://docs.moodle.org/26/en/Mobile_app_PUSH_Notifications (you can also check out the dev roadmap and track progress for PUSH notifications at http://docs.moodle.org/dev/Moodle_Mobile_Push_Notifications).
Will you use PUSH notifications on your Moodle site?
Update 2/5: 1.4 version of the app is not yet available, the docs are a work in progress as the mobile team works through some additional development.