Prefabrication by off-site manufacturing leads to a reduced overall construction schedule, improved quality, and reduced resource wastage. Modular building is therefore increasingly popular and promoted. With the recent promotion a number of relevant studies have been completed, however, a review of the design, construction, and performance of modular buildings under different loading conditions is lacking. This paper presents a state-of-the-art review of modular building structures. First, structural forms and construction materials are presented as a brief introduction to the modular structures. Modular building is shown to refer not to a single structure type, but a variety of structural systems and materials. These modular structures might perform differently to similar traditional structures and the structural performance is highly dependent on inter- and intra-module connections. The structural response of modules to different hazards is then considered, followed by the current design practice and methodology. As a currently developing area there is great potential for innovation in modular structures and several key research areas are identified for further work. •State-of-the-art review of modular building structures.•Structural connections are the key to overall performance.•Overview of the structural response to hazards including wind, earthquake and blast.•Key research areas are identified for further work.