Steel-concrete composite structures have been used in bridge engineering from decades. This is due to rational utilisation of the strength properties of the two materials. At the same time, the reinforced concrete (or prestressed) deck slab is more favourable than the orthotropic steel plate used in steel bridges (higher mass, better vibration damping, longer life). The most commonly found in practice are composite girder bridges, particularly in highway bridges of small and medium spans, but the spans may reach over 200 m. In larger spans steel truss girders are applied. Bridge composite structures are also employed in cable-stayed bridge decks of the main girder spans of the order of 600, 800 m. The aim of the article is to present the cionstruction process and strength analysis problems concerning of this type of structures. Much attention is paid to the design and calculation of the shear connectors characteristic for the discussed objects. The authors focused mainly on the issues of single composite structures. The effect of assembly states on the stresses and strains in composite members are highlighted. A separate part of problems is devoted to the influence of rheological factors, i.e. concrete shrinkage and creep, as well as thermal factors on the stresses and strains and redistribution of internal forces.