The Ancient Greeks developed astronomy, which they treated as a branch of mathematics, to a highly sophisticated level. The first geometrical, three-dimensional models to explain the apparent motion of the planets were developed in the 4th century BC by Eudoxus of Cnidus and Callippus of Cyzicus. Their models were based on nested homocentric spheres centered upon the Earth. Their younger contemporary Heraclides Ponticus proposed that the Earth rotates around its axis.

A different approach to celestial phenomena was taken by natural philosophers such as Plato and Aristotle. They were less concerned with developing mathematical predictive models than with developing an explanation of the reasons for the motions of the Cosmos. In his Timaeus, Plato described the universe as a spherical body divided into circles carrying the planets and governed according to harmonic intervals by a world soul. Aristotle, drawing on the mathematical model of Eudoxus, proposed that the universe was made of a complex system of concentric spheres, whose circular motions combined to carry the planets around the earth. This basic cosmological model prevailed, in various forms, until the 16th century AD.

In the 3rd century BC Aristarchus of Samos was the first to suggest a heliocentric system, although only fragmentary descriptions of his idea survive. Eratosthenes, using the angles of shadows created at widely separated regions, estimated the circumference of the Earth with great accuracy.

Greek geometrical astronomy developed away from the model of concentric spheres to employ more complex models in which an eccentric circle would carry around a smaller circle, called an epicycle which in turn carried around a planet. The first such model is attributed to Apollonius of Perga and further developments in it were carried out in the 2nd century BC by Hipparchus of Nicea. Hipparchus made a number of other contributions, including the first measurement of precession and the compilation of the first star catalog in which he proposed our modern system of apparent magnitudes.

The Antikythera mechanism, an ancient Greek astronomical observational device for calculating the movements of the Sun and the Moon, possibly the planets, dates from about 150–100 BC, and was the first ancestor of an astronomical computer. It was discovered in an ancient shipwreck off the Greek island of Antikythera, between Kythera and Crete. The device became famous for its use of a differential gear, previously believed to have been invented in the 16th century AD, and the miniaturization and complexity of its parts, comparable to a clock made in the 18th century. The original mechanism is displayed in the Bronze collection of the National Archaeological Museum of Athens, accompanied by a replica.

Depending on the historian's viewpoint, the acme or corruption of physical Greek astronomy is seen with Ptolemy of Alexandria, who wrote the classic comprehensive presentation of geocentric astronomy, the Megale Syntaxis (Great Synthesis), better known by its Arabic title Almagest, which had a lasting effect on astronomy up to the Renaissance. In his Planetary Hypotheses, Ptolemy ventured into the realm of cosmology, developing a physical model of his geometric system, in a universe many times smaller than the more realistic conception of Aristarchus of Samos four centuries earlier.