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. 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.