The pandemic virus COVID-19 has caused hundreds of millions of infections and deaths, resulting in enormous social and economic losses worldwide. As the virus strains continue to evolve, their ability to spread increases. The detection by reverse transcription polymerase chain reaction is time-consuming and less sensitive. As a result, X-ray images and computed tomography images started to be used in the diagnosis of COVID-19. Since the global outbreak, medical image processing researchers have proposed several automated diagnostic models in the hope of helping radiologists and improving diagnostic accuracy. This paper provides a systematic review of these diagnostic models from three aspects: image preprocessing, image segmentation, and classification, including the common problems and feasible solutions that encountered in each category. Furthermore, commonly used public COVID-19 datasets are reviewed. Finally, future research directions for medical image processing in managing COVID-19 are proposed.