This Element focuses on the most enduring project of the Babylonian astral sciences, namely the study of celestial signs, and addresses basic questions such as what constituted a sign, the parameters defining celestial signs, and the modalities of signs in terms of actual, possible, and conceivable phenomena. The science of signs, whether practiced in ancient Babylonia, Assyria, Hellenistic Greece or Rome, or in medieval Europe, where the ordo scientiarum included prognostic disciplines such as astrology and divination, and whether framed as the work of the gods or of nature, reflected the idea of an intelligible world. Commitment to the idea of the intelligibility of the world's phenomena is a feature of natural philosophy as well as of modern science. This Element shows it was also a signature of the Babylonian science of celestial signs.