Artificial Intelligence (AI) methods have significant potential for diagnosis and prognosis of COVID-19 infections. Rapid identification of COVID-19 and its severity in individual patients is expected to enable better control of the disease individually and at-large. There has been remarkable interest by the scientific community in using imaging biomarkers to improve detection and management of COVID-19. Exploratory tools such as AI-based models may help explain the complex biological mechanisms and provide better understanding of the underlying pathophysiological processes. The present review focuses on AI-based COVID-19 studies as applies to chest x-ray (CXR) and computed tomography (CT) imaging modalities, and the associated challenges. Explicit radiomics, deep learning methods, and hybrid methods that combine both deep learning and explicit radiomics have the potential to enhance the ability and usefulness of radiological images to assist clinicians in the current COVID-19 pandemic. The aims of this review are: first, to outline COVID-19 AI-analysis workflows, including acquisition of data, feature selection, segmentation methods, feature extraction, and multi-variate model development and validation as appropriate for AI-based COVID-19 studies. Secondly, existing limitations of AI-based COVID-19 analyses are discussed, highlighting potential improvements that can be made. Finally, the impact of AI and radiomics methods and the associated clinical outcomes are summarized. In this review, pipelines that include the key steps for AI-based COVID-19 signatures identification are elaborated. Sample size, non-standard imaging protocols, segmentation, availability of public COVID-19 databases, combination of imaging and clinical information and full clinical validation remain major limitations and challenges. We conclude that AI-based assessment of CXR and CT images has significant potential as a viable pathway for the diagnosis, follow-up and prognosis of COVID-19.