Asphaltene precipitation and deposition in the reservoir, near-wellbore region, and pipelines is one of the critical problems in flow assurance. It can cause a blockage of pore throats and reduce the permeability of the rock and the production rate in pipelines. Therefore, a thorough investigation of the structure and characterization of asphaltenes is essential to control this issue. Developing a reliable model to predict the deposition of asphaltenes in the reservoir and pipes is key to further understand this phenomenon. In this paper, the asphaltene structure is discussed in terms of the techniques used to identify the structure, molecular weight, size, and geometry of asphaltene. The thermodynamic characterization of asphaltenes is highly dependable upon the structure and molecular weight of particles; thus, a brief overview of the precipitation of asphaltenes is given. A detailed comparison of the available models in the literature is provided for asphaltene deposition in reservoirs as well as flowlines. Several mechanisms are assumed to develop current models; however, more research on dosure relationships and tuning parameters is needed because most of them are not universal and are dependent upon the conditions of the flow. The lack of complete data poses another challenge that hinders the ability to evaluate the accuracy of existing models. Industrial case studies and treatment methods are discussed to understand the application of the theories to practical issues and bridge the gap between theory and field conditions. Discoveries from the field and lab-scale experiments are provided in the paper to assist in addressing the mechanisms of the proposed models and the link between theory and application. Overall, this paper provides a comprehensive review of asphaltene deposition modeling and discusses potential improvements for current models.