The double-headed eagle is the symbol of orthodoxy of the Byzantine Empire and is still in use by the church, especially the Church of Greece and the Church of Russia. The heads of the eagles represent the dual sovereignity of the Byzantine Emperor; the left head representing Rome (the West) and the right head representing Constantinople (the East). In the claws of the eagle(s) are the cross and an orb.
Examples of double-headed eagle
The following gallery, shows examples of the double-headed eagle in the history of the church.