An arch bridge is a bridge with abutments at each end shaped as a curved arch. Arch bridges work by transferring the weight of the bridge and its loads partially into a horizontal thrust restrained by the abutments at either side, and partially into a vertical load on the arch supports. A viaduct (a long bridge) may be made from a series of arches, although other more economical structures are typically used today.

Possibly the oldest existing arch bridge is the Mycenaean Arkadiko Bridge in Greece from about 1300 BC. The stone corbel arch bridge is still used by the local populace. The well-preserved Hellenistic Eleutherna Bridge has a triangular corbel arch. The 4th century BC Rhodes Footbridge rests on an early voussoir arch.

Although true arches were already known by the Etruscans and ancient Greeks, the Romans were – as with the vault and the dome – the first to fully realize the potential of arches for bridge construction. A list of Roman bridges compiled by the engineer Colin O'Connor features 330 Roman stone bridges for traffic, 34 Roman timber bridges and 54 Roman aqueduct bridges, a substantial part still standing and even used to carry vehicles. A more complete survey by the Italian scholar Vittorio Galliazzo found 931 Roman bridges, mostly of stone, in as many as 26 countries (including former Yugoslavia).

Roman arch bridges were usually semicircular, although a number were segmental arch bridges (such as Alconétar Bridge), a bridge which has a curved arch that is less than a semicircle. The advantages of the segmental arch bridge were that it allowed great amounts of flood water to pass under it, which would prevent the bridge from being swept away during floods and the bridge itself could be more lightweight. Generally, Roman bridges featured wedge-shaped primary arch stones (voussoirs) of the same in size and shape. The Romans built both single spans and lengthy multiple arch aqueducts, such as the Pont du Gard and Segovia Aqueduct. Their bridges featured from an early time onwards flood openings in the piers, e.g. in the Pons Fabricius in Rome (62 BC), one of the world's oldest major bridges still standing.

Roman engineers were the first and until the Industrial Revolution the only ones to construct bridges with concrete, which they called Opus caementicium. The outside was usually covered with brick or ashlar, as in the Alcántara Bridge.

The Romans also introduced segmental arch bridges into bridge construction. The 330 m-long (1,080 ft) Limyra Bridge in southwestern Turkey features 26 segmental arches with an average span-to-rise ratio of 5.3:1, giving the bridge an unusually flat profile unsurpassed for more than a millennium. Trajan's bridge over the Danube featured open-spandrel segmental arches made of wood (standing on 40 m-high (130 ft) concrete piers). This was to be the longest arch bridge for a thousand years both in terms of overall and individual span length, while the longest extant Roman bridge is the 790 m-long (2,590 ft) long Puente Romano at Mérida. The late Roman Karamagara Bridge in Cappadocia may represent the earliest surviving bridge featuring a pointed arch.

In medieval Europe, bridge builders improved on the Roman structures by using narrower piers, thinner arch barrels and higher span-to-rise ratios on bridges. Gothic pointed arches were also introduced, reducing lateral thrust, and spans increased as with the eccentric Puente del Diablo (1282). With more advanced design and bridge-building techniques, the alternative informal name of Devil's Bridge became more widely used across Europe, because many people could not believe that these were man-made and capable of carrying the size of loads that they did.

The 14th century in particular saw bridge building reaching new heights. Span lengths of 40 m (130 ft), previously unheard of in the history of masonry arch construction, were now reached in places as diverse as Spain (Puente de San Martín), Italy (Castelvecchio Bridge) and France (Devil's bridge and Pont Grand) and with arch types as different as semi-circular, pointed and segmental arches. The bridge at Trezzo sull'Adda, destroyed in the 15th century, even featured a span length of 72 m (236 ft), not matched until 1796.