COVID-19 has evolved into one of the most severe and acute illnesses. The number of deaths continues to climb despite the development of vaccines and new strains of the virus have appeared. The early and precise recognition of COVID-19 are key in viably treating patients and containing the pandemic on the whole. Deep learning technology has been shown to be a significant tool in diagnosing COVID-19 and in assisting radiologists to detect anomalies and numerous diseases during this epidemic. This research seeks to provide an overview of novel deep learning-based applications for medical imaging modalities, computer tomography (CT) and chest X-rays (CXR), for the detection and classification COVID-19. First, we give an overview of the taxonomy of medical imaging and present a summary of types of deep learning (DL) methods. Then, utilizing deep learning techniques, we present an overview of systems created for COVID-19 detection and classification. We also give a rundown of the most well-known databases used to train these networks. Finally, we explore the challenges of using deep learning algorithms to detect COVID-19, as well as future research prospects in this field.