Engineers, architects, planners and designers must carefully consider the effects of wind in their work. Due to their slender and flexible nature, long-span bridges can often experience vibrations due to the wind, and so the careful analysis of wind effects is paramount. Traditionally, wind tunnel tests have been the preferred method of conducting bridge wind analysis. In recent times, owing to improved computational power, computational fluid dynamics simulations are coming to the fore as viable means of analysing wind effects on bridges. The focus of this paper is on long-span cable-supported bridges. Wind issues in long-span cable-supported bridges can include flutter, vortex-induced vibrations and rain–wind-induced vibrations. This paper presents a state-of-the-art review of research on the use of wind tunnel tests and computational fluid dynamics modelling of these wind issues on long-span bridges.