Objectives: To conduct a systematic survey of published techniques for automated diagnosis and prognosis of COVID-19 diseases using medical imaging, assessing the validity of reported performance and investigating the proposed clinical use-case. To conduct a scoping review into the authors publishing such work. Methods: The Scopus database was queried and studies were screened for article type, and minimum source normalized impact per paper and citations, before manual relevance assessment and a bias assessment derived from a subset of the Checklist for Artificial Intelligence in Medical Imaging (CLAIM). The number of failures of the full CLAIM was adopted as a surrogate for risk-of-bias. Methodological and performance measurements were collected from each technique. Each study was assessed by one author. Comparisons were evaluated for significance with a two-sided independent t-test. Findings: Of 1002 studies identified, 390 remained after screening and 81 after relevance and bias exclusion. The ratio of exclusion for bias was 71%, indicative of a high level of bias in the field. The mean number of CLAIM failures per study was 8.3 ± 3.9 [1,17] (mean ± standard deviation [min,max]). 58% of methods performed diagnosis versus 31% prognosis. Of the diagnostic methods, 38% differentiated COVID-19 from healthy controls. For diagnostic techniques, area under the receiver operating curve (AUC) = 0.924 ± 0.074 [0.810,0.991] and accuracy = 91.7% ± 6.4 [79.0,99.0]. For prognostic techniques, AUC = 0.836 ± 0.126 [0.605,0.980] and accuracy = 78.4% ± 9.4 [62.5,98.0]. CLAIM failures did not correlate with performance, providing confidence that the highest results were not driven by biased papers. Deep learning techniques reported higher AUC (p < 0.05) and accuracy (p < 0.05), but no difference in CLAIM failures was identified. Interpretation: A majority of papers focus on the less clinically impactful diagnosis task, contrasted with prognosis, with a significant portion performing a clinically unnecessary task of differentiating COVID-19 from healthy. Authors should consider the clinical scenario in which their work would be deployed when developing techniques. Nevertheless, studies report superb performance in a potentially impactful application. Future work is warranted in translating techniques into clinical tools.