Pedimental sculpture is a form of architectural sculpture designed for installation in the tympanum, the space enclosed by the architectural element called the pediment. Originally a feature of Ancient Greek architecture, pedimental sculpture started as a means to decorate a pediment in its simplest form: a low triangle, like a gable, above an horizontal base or entablature. However, as classical architecture developed from the basis of Ancient Greek and Roman architecture, the varieties of pedimental sculpture also developed. The sculpture can be either freestanding or relief sculpture, in which case it is attached to the back wall of the pediment. Harris in The Illustrated Dictionary of Historic Architecture defines pediment as "In classical architecture, the triangular gable end of the roof above the horizontal cornice, often filled with sculpture." Pediments can also be used to crown doors or windows.

In Romanesque architecture, and very often in Gothic architecture, the tympanum is usually semi-circular at the top, and the sculptural groups, usually with religious subjects, adapted to fit the new spaces. In the Renaissance triangular pediments returned, as gradually did sculptural groups within them, becoming very popular for important buildings in the 19th century.

The pediment begins in Ancient Greek architecture; according to the mid-fifth century BCE poet Pindar, it was a Corinthian invention. It is possible that it was devised specifically to contain sculpture, which from the early 6th century became "customary (though never obligatory)" in Doric temples; in Ionic ones it was a "rarity". A difference between the ancient Greek temple and temples of other, older, cultures of the Near East was that the visual effect and decoration of the exterior exceeded that of the interiors and exteriors behind the main facade. Like the other forms of exterior decoration such as statues, antefixes, and acroteria, the pedimental sculptures were originally in terracotta and coloured.

The "earliest pedimental composition to have survived," from the Early Archaic Period, was from the Temple of Artemis, Corfu, about 580–570 BCE. Large parts of the sculptural group are in the Archaeological Museum of Corfu, including the central figure of the winged gorgon Medusa, flanked by two crouching lions. Richter points out that the "weak points are the lack of concerted action and unity as well as the ludicrously small scale of the side figures compared with the central Gorgon."

Gorgons and gorgon heads were the most common early pedimental sculptures, as an architectural version of the gorgoneion apotropaic amulet, which both Athena and Zeus are said to have worn as a pendant. Greek temples with pediment sculptures usually had them at both ends of the temple, and tended to have contrasting scenes, one perhaps a peaceful scene with deities, and the other with a battle or dramatic scene from mythology.

Over the next decades refinements were made in the design and carving of pedimental sculpture, the small "Hydra pediment" in Athens (about 570 BCE), the "Bluebeard pediment from the 'old Athena temple' the Siphnian Treasury at Delphi (about 525 BCE), the Megarian Treasury at Olympia (about 520–510 BCE), the temple to Aphaia at Aigina (about 500–480 BCE), the Temple of Zeus at Olympia (about 465–460 BCE, the remains of the Eastern pediment of the Temple of Zeus at Olympia are in the site museum) and others, but "they did not satisfy the Greek sculptor for long." Finally, in the Parthenon pediments (about 438–432) "we reach the climax of Greek pedimental composition". After the Parthenon there is no outstanding pedimental composition, at least now known.

In the late or Hellenistic phase of Etruscan art, after about 300 BCE, Greek-style groups were introduced, but in terracotta rather than stone; some large fragments of these have survived. The Romans also used terracotta, but also stone for the grandest temples. An Amazonomachy in marble on the Temple of Apollo Sosianus in Rome, whose fragments were excavated in the 1930s, is thought to be a Greek work of the 5th century BCE, removed by the Romans from a temple there in the 1st century CE. Allusions to the recent Battle of Actium have been proposed. The group on the final rebuilding of the Capitoline Temple of Jupiter Optimus Maximus is known from literary descriptions and depictions in other works of art, but none of it is known to survive.

The Parthenon's west pediment depicted the contest between Athena and Poseidon over Attica and the east pediment the birth of Athena. Classical archeologists since Johann Joachim Winckelmann's Geschichte der Kunst des Alterthums (published 1764) have recognized Greek pediment sculpture, in particular the pediments of the Parthenon, as the standard of the highest-quality art in antiquity. For Martin Schede, writing in 1923, the remains of limestone pediments, although "badly shattered indeed," represented "the highest artistic achievement of two generations of a most artistic people," the value of which was impossible to overestimate. The travel writer Solomon Charles Kaines Smith specifically named the "Three Fates" of the east pediment the "highest surviving achievement of Greek sculpture," and for Wincklemann's contemporary Ennio Quirino Visconti the Parthenon pediments "met the criteria for the best artists of the best period." The Parthenon compositions are considered to be the magnum opus of Classical pedimental decoration.