Computed Tomography (CT) is a frequently utilized imaging technology that is employed in the clinical diagnosis of many disorders. However, clinical diagnosis, data storage, and management are posed huge challenges by a huge volume of non-homogeneous CT data in terms of imaging quality. As a result, the quality assessment of CT images is a crucial problem that demands consideration. The history, advancements in research, and current developments in CT image quality assessment (IQA) are examined in this paper. In this review, we collected and researched more than 500 CT-IQA publications published before August 2023. And we provide the visualization analysis of keywords and co-citations in the knowledge graph of these papers. Prospects and obstacles for the continued development of CT-IQA are also covered. At present, significant research branches in the CT-IQA domain include Phantom study, Artificial intelligence deep-learning reconstruction algorithm, Dose reduction opportunity, and Virtual monoenergetic reconstruction. Artificial intelligence (AI)-based CT-IQA also becomes a trend. It increases the accuracy of the CT scanning apparatus, amplifies the impact of the CT system reconstruction algorithm, and creates an effective algorithm for post-processing CT images. AI-based medical IQA offers excellent application opportunities in clinical work. AI can provide uniform quality assessment criteria and more comprehensive guidance amongst various healthcare facilities, and encourage them to identify one another's images. It will help lower the number of unnecessary tests and associated costs, and enhance the quality of medical imaging and assessment efficiency.