The artistic depiction of angels is rooted in their mission.
To understand the artistic depiction of angels, we must first understand the nature of an angel in the Christian tradition. First of all, the English word “angel” comes from the Latin angelus, meaning “messenger of God.” The Latin stems from Greek ἄγγελος ángelos, which is a translation of the Hebrew mal’ākh, meaning “messenger,” “delegate,” or “ambassador.”
The Catechism of the Catholic Church puts it this way:
St. Augustine says: “‘Angel’ is the name of their office, not of their nature. If you seek the name of their nature, it is ‘spirit’; if you seek the name of their office, it is ‘angel’: from what they are, ‘spirit,’ from what they do, ‘angel.’”
With their whole beings the angels are servants and messengers of God. Because they “always behold the face of my Father who is in heaven” they are the “mighty ones who do his word, hearkening to the voice of his word.”
The word “angel” then simply describes what they do and not what they are. Angels are above all messengers and as we will see when we open up Sacred Scripture, they are messengers of God’s divine plan. (CCC 329)
Angels are pure spirits, meaning that they do not posses a physical body, though at times they can take on the appearance of a human. The visible form that is often reported in Scripture or popular news stories is a facade, a mask they put on so that we can see them with our eyes. Otherwise they are naturally invisible creatures.
For the first few centuries of the Church angels were shown not much different from humans in religious art, basing their representations on what little is described in biblical accounts.
However, by the 4th century artists started to differentiate these spiritual creatures. The first known depiction of an angel with wings is on the Prince’s Sarcophagus, found at Sarigüzel, near Istanbul, and dated between 379 and 395.
Ever since, artists generally used wings and linked it to the mission of these creatures as messengers.
Part of the reason for the change in religious art is linked to the spiritual symbolism of birds. Birds in the ancient world were seen (and used) as messengers. The tradition is as ancient as Noah and continued through Greek mythology. The god Hermes, for example, is known as the messenger of the gods and was often depicted with wings attached to his helmet or hat. It was natural for Greco-Roman artists to draw upon this tradition to visually represent angels, the true messengers of God.
So while angels do not have wings, the artistic expression has become an excellent way to visualize their office entrusted to them by God.