Machine learning methods offer great promise for fast and accurate detection and prognostication of COVID-19 from standard-of-care chest radiographs (CXR) and computed tomography (CT) images. Many articles have been published in 2020 describing new machine learning-based models for both of these tasks, but it is unclear which are of potential clinical utility. In this systematic review, we search EMBASE via OVID, MEDLINE via PubMed, bioRxiv, medRxiv and arXiv for published papers and preprints uploaded from January 1, 2020 to October 3, 2020 which describe new machine learning models for the diagnosis or prognosis of COVID-19 from CXR or CT images. Our search identified 2,212 studies, of which 415 were included after initial screening and, after quality screening, 61 studies were included in this systematic review. Our review finds that none of the models identified are of potential clinical use due to methodological flaws and/or underlying biases. This is a major weakness, given the urgency with which validated COVID-19 models are needed. To address this, we give many recommendations which, if followed, will solve these issues and lead to higher quality model development and well documented manuscripts.