Since the first case of coronavirus disease 2019 (COVID-19) was discovered in December 2019, COVID-19 swiftly spread over the world. By the end of March 2021, more than 136 million patients have been infected. Since the second and third waves of the COVID-19 outbreak are in full swing, investigating effective and timely solutions for patients' check-ups and treatment is important. Although the SARS-CoV-2 virus-specific reverse transcription polymerase chain reaction test is recommended for the diagnosis of COVID-19, the test results are prone to be false negative in the early course of COVID-19 infection. To enhance the screening efficiency and accessibility, chest images captured via X-ray or computed tomography (CT) provide valuable information when evaluating patients with suspected COVID-19 infection. With advanced artificial intelligence (AI) techniques, AI-driven models training with lung scans emerge as quick diagnostic and screening tools for detecting COVID-19 infection in patients. In this article, we provide a comprehensive review of state-of-the-art AI-empowered methods for computational examination of COVID-19 patients with lung scans. In this regard, we searched for papers and preprints on bioRxiv, medRxiv, and arXiv published for the period from January 1, 2020, to March 31, 2021, using the keywords of COVID, lung scans, and AI. After the quality screening, 96 studies are included in this review. The reviewed studies were grouped into three categories based on their target application scenarios: automatic detection of coronavirus disease, infection segmentation, and severity assessment and prognosis prediction. The latest AI solutions to process and analyze chest images for COVID-19 treatment and their advantages and limitations are presented. In addition to reviewing the rapidly developing techniques, we also summarize publicly accessible lung scan image sets. The article ends with discussions of the challenges in current research and potential directions in designing effective computational solutions to fight against the COVID-19 pandemic in the future.