Epidemics have disturbed human lives for centuries causing massive numbers of deaths and illnesses among people and animals. As the number of urbanized and mobile population has increased, the possibility of a worldwide pandemic has grown too. The latest advances in high-performance computing and computational network science can help computational epidemiologists to develop large-scale high-fidelity models of epidemic spread. These models can help to characterize the large-scale patterns of epidemics and guide public health officials and policy makers in taking appropriate decisions to prevent and control such epidemics. This paper presents an overview of the epidemic spread modeling and simulation, and summarizes the main technical challenges in this field. It further investigates the most relevant recent approaches carried out towards this perspective and provides a comparison and classification of these approaches.