While there are no official Zotero apps for mobile devices, there are several third-party solutions.
BibUp helps you create bibliographic references by scanning books barcodes and extracts of text. The references, including the OCRed text, can be viewed on a web page and collected using the Zotero plugin for Firefox.
PaperShip makes it easy to to view and add to your library, read and annotate attachments, and share references. For Mac, iPhone, and iPad.
With ZotPad you can view and edit your library, as well as read and annotate attachments.
With Zandy you can view and edit your Zotero library on your Android device. http://www.gimranov.com/avram/w/zandy-user-guide
Zed and Zed Lite
View, edit, and add to your resource library on the go.
With Zojo you can view citations stored at Zotero on your Android phone, and download, annotate, and upload PDF attachments.
ZotFile is a Zotero plugin that syncs your library with your mobile PDF reader and extracts mobile annotations into Zotero notes.
To learn about new third-party apps for Zotero, see the Zotero for Mobile documentation pages.
While there is no official Zotero app at present, Zotero's website lists a number of third party apps that work with Zotero.
Zotero Reader (allows you to view your Zotero library, including attachments, in Android, iPad and desktop)
BibUp (allows you to add books to your library by scanning their ISBN barcodes)
PaperShip (allows you to view and add to your library, read and annotate attachments, and share references)
ZotPad (allows you to view and edit your library, as well as read and annotate attachments).
Scanner for Zotero (allows you to add books to your library by scanning their ISBN barcodes)
Zandy (view and edit your Zotero library)
Zotfile (a Zotero plugin that syncs your library with your mobile PDF reader and extracts mobile annotations into Zotero notes)