There is not currently a Zotero mobile app. The web library on zotero.org works well on mobile platforms, and you can use the Zotero bookmarklet (https://www.zotero.org/downloadbookmarklet) in your mobile web browser to save items to your library. A Zotero iPad app is in development.

On iPhone/iPad, there is a third-party app called Papership that was designed to work with both Mendeley and Zotero. Papership was bought by Elsevier several years ago, and it hasn't received much development attention since then. Users have reported problems with it working with current versions of Zotero, but you could try it and see if it works for you. If you are on Android, there are several other third-party apps that are actively being supported you could try (e.g., Zoo, Zotdroid).