Downbursts belong to sudden, local, and strong convection weather, which present significant destruction for structures. At any given time, there are approximately 2000 thunderstorms occurring on the Earth. Many studies have investigated the effects of downbursts on different structures. However, the extensive range of varying wind field parameters and the diverse representations of wind speeds render the study of structural wind effects complex and challenging under downbursts. This study firstly reviews the research of wind field properties of downbursts according to four common approaches, and the major findings, advantages, and disadvantages of which are concluded. Then, failure analysis of transmission line systems under stationary and moving downbursts is explored. The article also reviews the wind pressure on the roof of different kinds of low-rise buildings, and some dominant parameters, namely roof slope, distance of building from downburst center, wind direction angle, and so on, are discussed. Moreover, the wind effects caused by downbursts on high-rise buildings and some specialized structures are also considered because more and more wind hazards are related to downbursts. Finally, the limitations of the current study are pointed out, and recommendations for further research are given for the accurate assessment of the effects of wind on buildings, with a view to providing safer and more economical wind-resistant design solutions for structures.