Steel-concrete composite bridges, one of the sustainable structural forms, have excellent composite technical, economic and social results, and are increasingly popular in the bridge engineering. The steel-concrete composite structure can give full play to the material advantages of concrete and steel, and has been widely used in many fields of structural engineering, because of the reasonable load transfer, the economic efficiency, and the ease of construction. In order to accelerate bridge construction to assemblage, greening and intellectualization, promoting the use of steel-concrete composite structures in small and medium-span bridges faces opportunities and challenges. Two major categories, including research on commonly used shear connectors and steel-concrete composite girders in 2020, are collected, categorized and reviewed. Research on shear connectors covers the basic mechanical properties of stud connectors, PBL connectors, bolt connectors, and improved connectors, as well as the durability and degradation properties of connectors. Research on composite beams includes theoretical models, combined effects and spatial behavior, performance in the negative moment zone, dynamic characteristics of composite beams, deterioration performance, detection and reinforcement, construction methods.