This paper mainly reviews the progress of methods, and research development in the field of computed tomography(CT) with incomplete projection data, at home and abroad, on limited angle projection data reconstruction with the detector fully covered, and truncated data reconstruction with the detector partially covered. Firstly, the discrete model iterative reconstruction algorithm and the compressed sensing(CS) sampling reconstruction algorithm are discussed for the sparsely uniform and limited-view angle sampling in the case that the detector fully covers the detected object. Secondly, the reconstruction algorithm of back-projection filtration(BPF) for helical cone beam and improved ones for cone beam FDK are discussed in the case that the detector could not fully cover the detected object. This paper could provide the researchers in CT reconstruction field the criticism of methods and summaries. Furthermore, it also points out current focus of the study and the research direction in the future.