Fibre reinforced polymer composites, developed primarily for the aerospace and defence industries, are a class of materials with great potential to use in civil infrastructure. Since the construction of the first all-composite bridge superstructure in Miyun, China, in 1982, they have been gradually gaining acceptance from civil engineers as a new construction material. During these 30 years, their proved to be useful in a few areas of application: mostly in form of sheets and strips for strengthening existing bridge structures, and to some extent, as reinforcing bars substituting steel as concrete reinforcement. Also, a number of constructions have built, in which FRP composites replaced traditional materials for structural elements (girders, bridge decks, stay cables). Among these constructions there is a relatively big amount of hybrid bridge structures, where only a part of the superstructure is made of FRP composites, and a much smaller amount of all-composite bridge structures, with superstructures made exclusively of this material. The purpose of this paper is to present the state of the art in the use of FRP composites in bridge engineering with the focus on hybrid and all-composite structures. Firstly, the paper will present the basic information about FRP composites, including the definition, description of the components, mechanical properties and general areas of application. Then, it will focus on FRP composites as the material of which structural elements are made, describing manufacturing processes relevant to civil engineering applications, assortment of structural profiles, cables, tendons and bridge deck systems, presenting the problem of codes and design guidelines that refer to the use FRP composites as the construction material, and methods of joining structural elements. Thirdly, it will compare the properties of FRP composites with those of traditional materials. Finally, there are presented some examples of hybrid and allcomposite bridge structures and a list of 355 constructions made of this material around the world, with basic data and references providing more information.