Three-dimensional (3D) imaging faces challenges due to machine vision requiring complicated applications and diverse functionalities. Due to its compact structure and reliable performance, 3D imaging using single-camera stereo vision (SSV) offers a considerable approach to object reconstruction and situational awareness under spatially-limited conditions. In this paper, we demonstrated the theoretical basis for SSV-based 3D imaging. Next, we introduced 3D imaging techniques based on known or unknown camera motion, and those using reflective, refractive, or diffractive optical elements based on system setup, basic principle, and implementation methods. Furthermore, we analyzed existing methods based on their strengths and shortcomings in the field of view, spatial resolution, viewpoint flexibility, and dynamic response. Particularly, the calibration methods of misalignment parameters between the camera and optical element are reviewed to enhance 3D reconstruction accuracy. In addition to the technical challenges and potential applications, we discussed the development trends of SSV-based 3D imaging toward a wide field of view, high resolution, high dynamic and real-time capability, and strong environmental adaptability.