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.
You can connect to calibre using just Chrome or Firefox 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.