Chest X-rays (CXR) and computed tomography (CT) are the main medical imaging modalities used against the increased worldwide spread of the 2019 coronavirus disease (COVID-19) epidemic. Machine learning (ML) and artificial intelligence (AI) technology, based on medical imaging fully extracting and utilizing the hidden information in massive medical imaging data, have been used in COVID-19 research of disease diagnosis and classification, treatment decision-making, efficacy evaluation, and prognosis prediction. This review article describes the extensive research of medical image-based ML and AI methods in preventing and controlling COVID-19, and summarizes their characteristics, differences, and significance in terms of application direction, image collection, and algorithm improvement, from the perspective of radiologists. The limitations and challenges faced by these systems and technologies, such as generalization and robustness, are discussed to indicate future research directions.