The official Zotero apps for iPad and iPhone are available on the App Store.
While there is no official Android app for Zotero, the following are available:
Zoo for Zotero, by Michael Johnston
ZotEZ2, by EZBio.net
The mobile version of the Zotero web library also allows you to access and edit your Zotero library on your tablet or mobile phone.
You can also save items to your Zotero account using zotero.org/save.