Terahertz (THz) technology has broad prospect in the fields of next-generation mobile communications, radar imaging, material identification, atmospheric remote sensing, radio astronomy, etc.Among them, regulating devices that can actively manipulate the amplitude, frequency, and phase of THz waves have become one of the core components for the actual applications. Spatial terahertz modulator (STM), as a special representative of spatial wavefront control devices, has shown important applications in beam steering, beam scanning, beam forming, and even phase arrayed technology. This paper summarizes and analyzes the state-of-the-art of electronically controlled STM and optically controlled STM in recent years, with an emphasis on the semiconductor based all-optical STM because of its simple manufacture and low cost. This paper detailedly summarizes the modulation mechanism and simulation model of this kind of all-optical STM, systematically overviews the functional devices based on all-optical STM as well as the corresponding recent advances in THz imaging, discusses the technique limits of current STMs, and then introduces several new device architectures that have been proposed to enhance the modulation efficiency, reduce the device insertion loss, improve the laser utilization, increase the modulation speed, and so on. Finally, the development trend of optically controlled STMs is discussed.