calibre for iOS
calibre itself does not run on the iPhones/iPad, but you can connect to calibre running on your mac, read books and manage your library in several ways.
The easiest way to transfer books wirelessly to your iPhone/iPad is to use the Calibre Companion iOS app. Calibre Companion allows calibre to connect to your iPhone/iPad wirelessly, just as though you had plugged it in 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 Safari 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.