The advent of the coronavirus pandemic has sparked the interest in predictive models capable of forecasting virus-spreading, especially for boosting and supporting decision-making processes. In this paper, we will outline the main Deep Learning approaches aimed at predicting the spreading of a disease in space and time. The aim is to show the emerging trends in this area of research and provide a general perspective on the possible strategies to approach this problem. In doing so, we will mainly focus on two macro-categories: classical Deep Learning approaches and Hybrid models. Finally, we will discuss the main advantages and disadvantages of different models, and underline the most promising development directions to improve these approaches.