Computational imaging is an imaging technology that not only relies on optical physical devices, but also relies on optical modulation and reconstruction algorithm. It provides new ideas for breaking through the limitations of traditional imaging systems in terms of temporal and spatial resolution and detection sensitivity. Computational ghost imaging (CGI) is one of the fastest-growing branches in the field of computational imaging, it has been widely used in single-pixel imaging, super-resolution imaging, biomedicine, information encryption, lidar, and information transmission under turbulence in recent years. In this paper, we summarize the progress of construction methods of illumination patterns and image reconstruction algorithms, which are two key technologies that affect quality of CGI. We mainly introduce the construction methods of random matrix, the orderly Hadamard matrix, orthogonal transformation matrix, and discuss the imaging performance of various illumination patterns under traditional correlation reconstruction algorithms and novel deep learning reconstruction algorithms. Finally, the construction methods of illumination patterns and reconstruction algorithms are summarized, and the development prospect of CGI technology is also discussed.