There are multiple ways to classify an arch:
199 by the geometrical shape of its intrados (for example, semicircular, triangular, etc.);
299 for the arches with rounded intrados, by the number of circle segments forming the arch (for example, round arch is single-centred, pointed arch is two-centred);
399 by the material used (stone, brick, concrete, steel) and construction approach. For example, the wedge-shaped voussoirs of a brick arch can be made by cutting the regular bricks ("axed brick" arch) or manufactured in the wedge shape ("gauged brick" arch);
499 structurally, by the number of hinges (movable joints) between solid components. For example, voussoirs in a stone arch should not move, so these arches usually have no hinges (are "fixed"). Permitting some movement in a large structure allows to alleviate stresses (caused, for example, by the thermal expansion), so many bridge spans are built with three hinges (one at each support and one at the crown) since the mid-19th century.

A sequence of arches can be grouped together forming an arcade. Romans perfected this form, as shown, for example, by arched structures of Pont du Gard. In the interior of hall churches, arcades of separating arches were used to separate the nave of a church from the side aisle, or two adjacent side aisles.

Two-tiered arches, with two arches superimposed, were sometimes used in Islamic architecture, mostly for decorative purposes.

An opening of the arch can be filled, creating a blind arch. Blind arches are frequently decorative, and were extensively used in Early Christian, Romanesque, and Islamic architecture. Alternatively, the opening can be filled with smaller arches, producing a containing arch, common in Gothic and Romanesque architecture. Multiple arches can be superimposed with an offset, creating an interlaced series of usually (with some exceptions) blind and decorative arches. Most likely of Islamic origin, the interlaced arcades were popular in Romanesque and Gothic architecture. Rear-arch (also rere-arch) is the one that frames the internal side of an opening in the external wall.
• Arcades of Pont du Gard (Roman)
• Separating arches in the St. Zeno church [de]
• Two-tiered arches in the Mosque-Cathedral of Córdoba (Islamic)
• Large blind arch containing three smaller blind arches
• Interlaced arcade of blind arches at Castle Acre (Romanesque)
• Rear arch around three lights at St Matthew's Church, Langford
Structurally, relieving arches (often blind or containing) can be used to take off load from some portions of the building (for example, to allow use of thinner exterior walls with larger window openings, or, as in the Roman Pantheon, to redirect the weight of the upper structures to particular strong points). Transverse arches, introduced in Carolingian architecture, are placed across the nave to compartmentalize (together with longitudinal separating arches) the internal space into bays and support vaults. A diaphragm arch similarly goes in the transverse direction, but carries a section of wall on top. It is used to support or divide sections of the high roof. Strainer arches were built as an afterthought to prevent two adjacent supports from imploding due to miscalculation. Frequently they were made very decorative, with one of the best examples provided by the Wells Cathedral. Strainer arches can be "inverted" (upside-down) while remaining structural. When used across railway cuttings to prevent collapse of the walls, strainer arches may be referred to as flying arches. A counter-arch is built adjacent to another arch to oppose its horizontal action or help to stabilize it, for example, when constructing a flying buttress.
• Relieving blind arches made of bricks at the Roman Pantheon
• Transverse arches in Speyer Cathedral
• Diaphragm arch in San Miniato al Monte
• "Scissors" strainer arch arrangement in Wells Cathedral includes an inverted arch

The large variety of arch shapes (left) can mostly be classified into three broad categories: rounded, pointed, and parabolic.
"Round" semicircular arches were commonly used for ancient arches that were constructed of heavy masonry, and were relied heavily on by the Roman builders since the 4th century BC. It is considered to be the most common arch form, characteristic for Roman, Romanesque, and Renaissance architecture.

A segmental arch, with a rounded shape that is less than a semicircle, is very old (the versions were cut in the rock in Ancient Egypt c. 2100 BC at Beni Hasan). Since then it was occasionally used in Greek temples, utilized in Roman residential construction, Islamic architecture, and got popular as window pediments during the Renaissance.

A basket-handle arch (also known as depressed arch, three-centred arch, basket arch) consists of segments of three circles with origins at three different centers (sometimes uses five or seven segments, so can also be five-centred, etc.). Was used in late Gothic and Baroque architecture.

A horseshoe arch (also known as keyhole arch) has a rounded shape that includes more than a semicircle, is associated with Islamic architecture and was known in areas of Europe with Islamic influence (Spain, Southern France, Italy). Occasionally used in Gothics, it briefly enjoyed popularity as the entrance door treatment in the interwar England.
• Semi-circular arches using brick and/or stone block construction at the Great Wall, China
• Segmental arch of the Alconétar Bridge
• Bridge with a basket handle arch
• Horseshoe arch in the Great Mosque of Cordoba
A pointed arch consists of two ("two-centred arch" ) or more circle segments culminating in a point at the top. It originated in the Islamic architecture, arrived in Europe in the second half of the 11th century (Cluny Abbey) and later became prominent in the Gothic architecture. The advantages of a pointed arch over a semicircular one are flexible ratio of span to rise and lower horizontal reaction at the base. This innovation allowed for taller and more closely spaced openings, which are typical of Gothic architecture. Equilateral arch is the most common form of the pointed arch, with the centers of two circles forming the intrados coinciding with the springing points of the opposite segment. Together with the apex point, they form a equilateral triangle, thus the name. If the centers of circles are farther apart, the arch becomes a narrower and sharper lancet arch that appeared in France in the Early Gothic architecture (Saint-Denis Abbey) …

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