Overview: More than 80% of human perception of external information comes from vision, and acquiring more information about the objective world is the eternal goal of human pursuit. Conventional optical imaging is essentially a process of recording and reproducing the intensity signal of a scene in the spatial dimension with direct uniform sampling. Therefore, the resolution and information content of imaging are inevitably constrained by several physical limitations such as optical diffraction limit, and spatial bandwidth product of the imaging system. How to break these physical limitations and obtain higher resolution and broader image field of view has been an eternal topic in this field. Computational optical imaging, by combining front-end optical modulation with back-end signal processing, offers a new approach to surpassing the diffraction limit of imaging systems and realizing super-resolution imaging. Although synthetic aperture techniques first exploited the idea of computational optical imaging to achieve resolution enhancement, they have never been encapsulated as a system in computational optical imaging. In this paper, we introduce the relevant research efforts on improving imaging resolution and expanding the spatial bandwidth product through computational optical synthetic aperture imaging, including the basic theory and technologies based on coherent active synthetic aperture imaging and incoherent passive synthetic aperture imaging. Furthermore, this paper reveals the pressing demand for "incoherent, passive, and beyond-diffraction-limit" imaging, identifies the bottlenecks, and provides an outlook on future research directions and potential technical approaches to address these challenges. The rapidly advancing computational imaging technology has provided new ideas, methods, and theories for far-field synthetic aperture detection. It significantly enhances the imaging efficiency of traditional synthetic aperture techniques and reduces excessive reliance on "interferometric phase acquisition" in synthetic aperture technology. It breaks through the functional/performance boundaries that traditional synthetic aperture technology can achieve and provides possibilities for extensive expansion and extension in the field of far-field synthetic aperture. Within the current computational imaging system, there are still a series of new concepts and new imaging techniques that are being perfected. It can be anticipated that as a branch of computational imaging, far-field optical synthetic aperture detection technology will undoubtedly experience rapid development and bring forth more possibilities in remote sensing, military reconnaissance, and near-Earth satellite detection, among other fields.