Coronavirus disease (COVID-19) is an infectious disease caused by a newly discovered coronavirus. The disease presents with symptoms such as shortness of breath, fever, dry cough, and chronic fatigue, amongst others. The disease may be asymptomatic in some patients in the early stages, which can lead to increased transmission of the disease to others. This study attempts to review papers on the role of imaging and medical image computing in COVID-19 diagnosis. For this purpose, PubMed, Scopus and Google Scholar were searched to find related studies until the middle of 2021. The contribution of this study is four-fold: 1) to use as a tutorial of the field for both clinicians and technologists, 2) to comprehensively review the characteristics of COVID-19 as presented in medical images, 3) to examine automated artificial intelligence-based approaches for COVID-19 diagnosis, 4) to express the research limitations in this field and the methods used to overcome them. Using machine learning-based methods can diagnose the disease with high accuracy from medical images and reduce time, cost and error of diagnostic procedure. It is recommended to collect bulk imaging data from patients in the shortest possible time to improve the performance of COVID-19 automated diagnostic methods.