calibre for Android
calibre itself does not run on phones/tablets but you can connect to calibre running on your home computer, read books and manage your library in several ways.
Connect with a USB cable
Simply plug in your phone/tablet into the computer with calibre running on it. It will show up in calibre as a device and you can manage the books on it.
The easiest way to transfer books wirelessly to your Android device is to use the Calibre Companion Android app. This app allows calibre to connect to your Android device wirelessly, just as though you plugged in the device with a USB cable. You can browse files on the device in calibre and use the Send to device button to transfer files to your device wirelessly.
You can also connect to calibre using just Chrome on the phone, and manage your collection and even read books in the browser, using the calibre Content server. To learn how to do this, see the User Manual.