An exedra (pl. exedras or exedrae) is a semicircular architectural recess or platform, sometimes crowned by a semi-dome, and either set into a building's façade or free-standing. The original Greek word ἐξέδρα ('a seat out of doors') was applied to a room that opened onto a stoa, ringed with curved high-backed stone benches, a suitable place for conversation. An exedra may also be expressed by a curved break in a colonnade, perhaps with a semicircular seat.

The exedra would typically have an apsidal podium that supported the stone bench. The free-standing (open air) exedra, often supporting bronze portrait sculpture, is a familiar Hellenistic structure, characteristically sited along sacred ways or in open places in sanctuaries, such as at Delos or Epidaurus. Some Hellenistic exedrae were built in relation to a city's agora, as in Priene. Monument architects have also used this free-standing style in modern times.

The exedra achieved particular popularity in ancient Roman architecture during the Roman Empire. In the 1st century AD, Nero's architects incorporated exedrae throughout the planning of his Domus Aurea, enriching the volumes of the party rooms, a part of what made Nero's palace so breathtakingly pretentious to traditional Romans, for no one had ever seen domes and exedrae in a dwelling before.

An exedra was normally a public feature: when rhetoricians and philosophers disputed in a Roman gymnasium it was in an exedra opening into the peristyle that they gathered. A basilica featured a large exedra at the far end from its entrance, where the magistrates sat, usually raised up several steps, in hearing cases. This was called a tribuna in Latin, and tribune is used for an area of raised floor backing onto a wall, often in an exedra.

Following precedents from Rome, exedrae continued to be in widespread use architecturally after the fall of Rome. In Byzantine architecture and Romanesque architecture, this familiar feature developed into the apse and is fully treated there.

The term exedra is still often used for secondary apses or niches in the more complicated plans of later Byzantine churches; another term is conch, named for the scallop shell form often taken by the half-dome cap. A famous use of the exedra is in Donato Bramante's Cortile del Belvedere extension of the Vatican Palace; that exedra was initially open to the sky.

In Muslim architecture, the exedra becomes a mihrab and invariably retains religious associations, wherever it is seen, even on the smallest scale, as a prayer niche.

Both Baroque and Neoclassical architecture used exedrae. Baroque architects, (for example, Pietro da Cortona in his Villa Pigneto), used them to enrich the play of light and shade and give rein to expressive volumes; Neoclassical architects, to articulate the rhythmic pacing of a wall elevation.