Whereas modern digital cameras use a pixelated detector array to capture images, single-pixel imaging reconstructs images by sampling a scene with a series of masks and associating the knowledge of these masks with the corresponding intensity measured with a single-pixel detector. Though not performing as well as digital cameras in conventional visible imaging, single-pixel imaging has been demonstrated to be advantageous in unconventional applications, such as multi-wavelength imaging, terahertz imaging, X-ray imaging, and three-dimensional imaging. The developments and working principles of single-pixel imaging are reviewed, a mathematical interpretation is given, and the key elements are analyzed. The research works of three-dimensional single-pixel imaging and their potential applications are further reviewed and discussed.