The new coronavirus disease (COVID-19) has been declared a pandemic since March 2020 by the World Health Organization. It consists of an emerging viral infection with respiratory tropism that could develop atypical pneumonia. Experts emphasize the importance of early detection of those who have the COVID-19 virus. In this way, patients will be isolated from other people and the spread of the virus can be prevented. For this reason, it has become an area of interest to develop early diagnosis and detection methods to ensure a rapid treatment process and prevent the virus from spreading. Since the standard testing system is time-consuming and not available for everyone, alternative early-screening techniques have become an urgent need. In this study, the approaches used in the detection of COVID-19 based on deep learning (DL) algorithms, which have been popular in recent years, have been comprehensively discussed. The advantages and disadvantages of different approaches used in literature are examined in detail. The Computed Tomography of the chest and X-ray images give a rich representation of the patient's lung that is less time-consuming and allows an efficient viral pneumonia detection using the DL algorithms. The first step is the pre-processing of these images to remove noise. Next, deep features are extracted using multiple types of deep models (pre-trained models, generative models, generic neural networks, etc.). Finally, the classification is performed using the obtained features to decide whether the patient is infected by coronavirus or it is another lung disease. In this study, we also give a brief review of the latest applications of cough analysis to early screen the COVID-19, and human mobility estimation to limit its spread.