This article presents a systematic overview of artificial intelligence (AI) and computer vision strategies for diagnosing the coronavirus disease of 2019 (COVID-19) using computerized tomography (CT) medical images. We analyzed the previous review works and found that all of them ignored classifying and categorizing COVID-19 literature based on computer vision tasks, such as classification, segmentation, and detection. Most of the COVID-19 CT diagnosis methods comprehensively use segmentation and classification tasks. Moreover, most of the review articles are diverse and cover CT as well as X-ray images. Therefore, we focused on the COVID-19 diagnostic methods based on CT images. Well-known search engines and databases such as Google, Google Scholar, Kaggle, Baidu, IEEE Xplore, Web of Science, PubMed, ScienceDirect, and Scopus were utilized to collect relevant studies. After deep analysis, we collected 114 studies and reported highly enriched information for each selected research. According to our analysis, AI and computer vision have substantial potential for rapid COVID-19 diagnosis as they could significantly assist in automating the diagnosis process. Accurate and efficient models will have real-time clinical implications, though further research is still required. Categorization of literature based on computer vision tasks could be helpful for future research; therefore, this review article will provide a good foundation for conducting such research.