The Tetrabiblos left Alexandria on the same transmission route as most of Ptolemy's other work: Byzantine Greek copyists kept it in circulation through the medieval Eastern Roman Empire, while in the ninth century Baghdad's translation movement rendered it into Arabic, where it entered a living astrological practice already absorbing Persian and Indian material. Arabic astrologers wrote extensive commentaries on it, and it was chiefly through Arabic intermediaries, along with direct Byzantine Greek manuscripts recovered later, that the text reached Latin Christian Europe.
By the high and late Middle Ages, the Tetrabiblos held something close to textbook status at European universities that taught astrology alongside medicine and astronomy, and Renaissance humanists produced fresh Greek to Latin translations once Byzantine scholars and manuscripts arrived in Italy after Constantinople's fall in 1453. Commentary on the text became a standard genre in its own right, with astrologers across four centuries and three linguistic traditions, Greek, Arabic and Latin, treating it as the authority to be glossed rather than argued past.
Much of what a modern Western astrologer would recognize, the classical planetary rulerships of the zodiac signs, the language of dignity and detriment, the emphasis on aspects between planets, either originates in the Tetrabiblos or was consolidated there from earlier Hellenistic sources now largely lost. Its influence is why the text is still read today, not as a historical curiosity alone but as the direct ancestor of a living technical vocabulary.