This paper investigates cases of anomalous aerial phenomena, abductions, and mysterious technologies depicted in ancient Greek mythology from a twenty-first century perspective, and in view of their commonality with occurrences observed worldwide and documented as Unidentified Anomalous Phenomena. The interdisciplinary approach aims to show that the descriptions of aerial phenomena and advanced technologies in ancient Greek myths are not solely the products of imagination but, perhaps, the rudimentary accounts of empirical observation of historical events expressed in a context of limited understanding of science and technology. The main themes of Classical Greek mythology are discussed, and their relation to the religious beliefs of the period. Key elements in the myth of The Abduction of Europe, and the myth of The Golden Fleece, point to the nation-building component of the ancient Greek mythical aerial phenomena.