Spatial hearing refers to the subjective perceptions of the spatial attributes of sound and is one of the important functions of human hearing. Based on the principles of spatial hearing, virtual auditory displays simulate the binaural signals in various acoustic environments and then create desired spatial auditory events via headphone or sometimes loudspeaker presentations. HRTF-based (head-related transfer functions) binaural synthesis is the core of virtual auditory displays over headphones. As a special spatial sound technique, virtual auditory displays are not only applicable to conventional audio reproduction, but also to a wide field of research areas and engineering applications, such as multimedia, virtual reality, communication, and acoustic environment assessments. During the past two or three decades, virtual auditory displays have become a hot topic in the field of acoustics and signal processing. This presentation first outlines the principles of spatial hearing, and then comprehensively reviews the principles, progresses, and applications of virtual auditory displays, including some recent works from the authors' research groups. Finally, the presentation will conclude with some prospective future works.