The outbreak of novel coronavirus disease (COVID- 19) has claimed millions of lives and has affected all aspects of human life. This paper focuses on the application of deep learning (DL) models to medical imaging and drug discovery for managing COVID-19 disease. In this article, we detail various medical imaging-based studies such as X-rays and computed tomography (CT) images along with DL methods for classifying COVID-19 affected versus pneumonia. The applications of DL techniques to medical images are further described in terms of image localization, segmentation, registration, and classification leading to COVID-19 detection. The reviews of recent papers indicate that the highest classification accuracy of 99.80% is obtained when InstaCovNet-19 DL method is applied to an X-ray dataset of 361 COVID-19 patients, 362 pneumonia patients and 365 normal people. Furthermore, it can be seen that the best classification accuracy of 99.054% can be achieved when EDL_COVID DL method is applied to a CT image dataset of 7500 samples where COVID-19 patients, lung tumor patients and normal people are equal in number. Moreover, we illustrate the potential DL techniques in drug or vaccine discovery in combating the coronavirus. Finally, we address a number of problems, concerns and future research directions relevant to DL applications for COVID-19.