This paper provides an overview of building structure modeling and control under bidirectional seismic waves. It focuses on different types of bidirectional control devices, control strategies, and bidirectional sensors used in structural control systems. This paper also highlights the various issues like system identification techniques, the time-delay in the system, estimation of velocity and position from acceleration signals, and optimal placement of the sensors and control devices. The importance of control devices and its applications to minimize bidirectional vibrations has been illustrated. Finally, the applications of structural control systems in real buildings and their performance have been reviewed.