The first bridges were spans made of wooden logs or planks and eventually stones, using a simple support and crossbeam arrangement.

The arch was first used by the Roman Empire for bridges and aqueducts, some of which still stand today. The Romans also used cement, which reduced the variation of strength found in natural stone. Brick and mortar bridges were built after the Roman era, as the technology for cement was lost then later rediscovered.

Rope bridges, a simple type of suspension bridge, were used by the Inca civilization in the Andes mountains of South America, just prior to European colonization in the 1500s.

During the 18th century there were many innovations in the design of timber bridges by Hans Ulrich, Johannes Grubenmann, and others. The first engineering book on building bridges was written by Hubert Gautier in 1716.

With the Industrial Revolution in the 19th century, truss systems of wrought iron were developed for larger bridges, but iron did not have the tensile strength to support large loads. With the advent of steel, which has a high tensile strength, much larger bridges were built, many using the ideas of Gustave Eiffel.

Bridges may be classified by how the four forces of tension, compression, bending and shear are distributed through their structure. Most bridges will employ all of the principle forces to some degree, but only a few will predominate. The separation of forces may be quite clear. In a suspension or cable-stayed span, the elements in tension are distinct in shape and placement. In other cases the forces may be distributed among a large number of members, as in a truss, or not clearly discernible to a casual observer as in a box beam. Bridges can also be classified by their lineage, which is shown as the vertical axis on the diagram to the right.

A bridge's structural efficiency may be considered to be the ratio of load carried to bridge weight, given a specific set of material types. In one common challenge students are divided into groups and given a quantity of wood sticks, a distance to span, and glue, and then asked to construct a bridge that will be tested to destruction by the progressive addition of load at the center of the span. The bridge taking the greatest load is by this test the most structurally efficient. A more refined measure for this exercise is to weigh the completed bridge rather than measure against a fixed quantity of materials provided and determine the multiple of this weight that the bridge can carry, a test that emphasizes economy of materials and efficient glue joints (see ''balsa wood bridge'').

A bridge's economic efficiency will be site and traffic dependent, the ratio of savings by having a bridge (instead of, for example, a ferry, or a longer road route) compared to its cost. The lifetime cost is composed of materials, labor, machinery, engineering, cost of money, insurance, maintenance, refurbishment, and ultimately, demolition and associated disposal, recycling, and reuse. Bridges employing only compression are relatively inefficient structurally, but may be highly cost efficient where suitable materials are available near the site and the cost of labor is low. For medium spans, trusses or box beams are usually most economical, while in some cases, the appearance of the bridge may be more important than its cost efficiency. The longest spans usually require suspension bridges.