The World Health Organization (WHO) declared a pandemic in response to the coronavirus COVID-19 in 2020, which resulted in numerous deaths worldwide. Although the disease appears to have lost its impact, millions of people have been affected by this virus, and new infections still occur. Identifying COVID-19 requires a reverse transcription-polymerase chain reaction test (RT-PCR) or analysis of medical data. Due to the high cost and time required to scan and analyze medical data, researchers are focusing on using automated computer-aided methods. This review examines the applications of deep learning (DL) and machine learning (ML) in detecting COVID-19 using medical data such as CT scans, X-rays, cough sounds, MRIs, ultrasound, and clinical markers. First, the data preprocessing, the features used, and the current COVID-19 detection methods are divided into two subsections, and the studies are discussed. Second, the reported publicly available datasets, their characteristics, and the potential comparison materials mentioned in the literature are presented. Third, a comprehensive comparison is made by contrasting the similar and different aspects of the studies. Finally, the results, gaps, and limitations are summarized to stimulate the improvement of COVID-19 detection methods, and the study concludes by listing some future research directions for COVID-19 classification.