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Coronavirus disease, first detected in late 2019 (COVID-19), has spread fast throughout the world, leading to high mortality. This condition can be diagnosed using RT-PCR technique on nasopharyngeal and throat swabs with sensitivity values ranging from 30 to 70%. However, chest CT scans and X-ray images have been reported to have sensitivity values of 98 and 69%, respectively. The application of machine learning methods on CT and X-ray images has facilitated the accurate diagnosis of COVID-19. In this study, we reviewed studies which used machine and deep learning methods on chest X-ray images and CT scans for COVID-19 diagnosis and compared their performance. The accuracy of these methods ranged from 76% to more than 99%, indicating the applicability of machine and deep learning methods in the clinical diagnosis of COVID-19.