MobileOrg is the name of the mobile companion app for Org mode, currently available for iOS and for Android. MobileOrg offers offline viewing and capture support for an Org mode system rooted on a “real” computer. It does also allow you to record changes to existing entries.
The iOS implementation for the iPhone/iPod Touch/iPad series of devices, was developed by Richard Moreland. Android users should check out MobileOrg Android by Matt Jones. The two implementations are not identical but offer similar features.
Chapter 15 of the manual
Appendix B of the manual
Key reference card