Pulmonary medical image analysis using image processing and deep learning approaches has made remarkable achievements in the diagnosis, prognosis, and severity check of lung diseases. The epidemic of COVID-19 brought out by the novel coronavirus has triggered a critical need for artificial intelligence assistance in diagnosing and controlling the disease to reduce its effects on people and global economies. This study aimed at identifying the various COVID-19 medical imaging analysis models proposed by different researchers and featured their merits and demerits. It gives a detailed discussion on the existing COVID-19 detection methodologies (diagnosis, prognosis, and severity/risk detection) and the challenges encountered for the same. It also highlights the various preprocessing and post-processing methods involved to enhance the detection mechanism. This work also tries to bring out the different unexplored research areas that are available for medical image analysis and how the vast research done for COVID-19 can advance the field. Despite deep learning methods presenting high levels of efficiency, some limitations have been briefly described in the study. Hence, this review can help understand the utilization and pros and cons of deep learning in analyzing medical images.