Zotero released a new first-party mobile app for iOS users on March 18th, 2022. It is available via the Apple App Store.
Though the mobile app looks slightly different from the desktop application, you may recognize that it emulates the current web library view almost exactly. That means you can use Zotero for iOS basically the same way as you would the web library. This includes viewing your items, attachments, and notes, as well as adding new notes and items, and even generating bibliographies from your collections!
The Zotero community has developed a "bookmarklet" to assist researchers while browsing content on a variety of mobile devices. In general, the features of the bookmarklet version are more limited than Zotero Standalone or Zotero for Firefox. The primary use of the bookmarklet is to save whatever page you are reading to your Zotero library for reference later.
The process for installing and using the Zotero bookmarklet varies depending on the browser you are using. Currently, the Zotero bookmarklet feature is available for the following platforms and devices:
Zotero is now available for iOS devices on the Apple app store
If you are on an Android or other mobile device, there are currently no first-party apps.
To use Zotero with a non-iOS mobile browser you will need to use the Zotero Bookmarklet:
For platform and device specific instructions, visit the official Zotero Bookmarklet page (https://www.zotero.org/downloadbookmarklet).
After following the instructions, you can visit any webpage on the device and save captured bibliographic information and a snapshot of the webpage you are viewing to your Zotero library by clicking on a "Save to Zotero" bookmark.
Third-party apps (generally, not officially supported by Zotero) are available for different devices. Zotero maintains a list of several solutions on their Zotero for Mobile Support page (https://www.zotero.org/support/mobile).