You can read the official announcement about version 3's release on Steam's website, for more details. The APK will be saved in your phone's Download folder. Go to the APK page, it should list the Steam app, long press on it and tap save to downloads. Long press on it and select Export to Storage. Open the app and navigate to Apps > Users page, and look for the Steam app. Android users can backup the current version (v 2.3.13) of the Steam app by extracting the APK with a tool such as APK Explorer & Editor (open source). However, if you update to the new version, and want to go back, you can only do so by using an APK of the old version. If you don't like the new app, you can disable automatic updates for it, and continue using it until Steam decides to end support for the old version. The app will ask you to login after updating to the new version, but don't be alarmed if it doesn't ask you to enter the Steam Guard code, it recognizes your device from the previous version. Download the new Steam mobile app from the Google Play Store, the iOS App Store or directly from Steam.

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