A COVID-19 diagnosis is primarily determined by RT-PCR or rapid lateral-flow testing, although chest imaging has been shown to detect manifestations of the virus. This article reviews the role of imaging (CT and X-ray), in the diagnosis of COVID-19, focusing on the published studies that have applied artificial intelligence with the purpose of detecting COVID-19 or reaching a differential diagnosis between various respiratory infections. In this study, ArXiv, MedRxiv, PubMed, and Google Scholar were searched for studies using the criteria terms 'deep learning', 'artificial intelligence', 'medical imaging', 'COVID-19' and 'SARS-CoV-2'. The identified studies were assessed using a modified version of the Transparent Reporting of a Multivariable Prediction Model for Individual Prognosis or Diagnosis (TRIPOD). Twenty studies fulfilled the inclusion criteria for this review. Out of those selected, 11 papers evaluated the use of artificial intelligence (AI) for chest X-ray and 12 for CT. The size of datasets ranged from 239 to 19,250 images, with sensitivities, specificities and AUCs ranging from 0.789-1.00, 0.843-1.00 and 0.850-1.00. While AI demonstrates excellent diagnostic potential, broader application of this method is hindered by the lack of relevant comparators in studies, sufficiently sized datasets, and independent testing.