Asphaltenes are the heaviest crude oil fraction and tend to self-associate and precipitate. The precipitation and deposition of asphaltenes during the production, refining, transportation of oil is the main for the oil industry, the precipitation of asphaltenes and their subsequent deposition can cause problems at all stages of production. Asphaltenes have different structures and molecular composition, they are a mixture of poorly defined components, they are self-associated even at very low concentrations, what makes them one of the most difficult components of crude oil. Since the deposition mechanism of paraffin wax differs from the deposition mechanism of asphaltenes, mathematical modeling of crystallization of paraffin will be considered separately in another work. Creating accurate asphaltene models that can predict the behavior of asphaltenes in various scenarios should help reduce asphaltene problems. This review is specifically devoted to advances in mathematical modeling of asphaltenes. Several different models have been proposed in the literature for predicting the initial conditions and precipitation of asphaltenes. Existing modeling approaches can be broadly classified into colloidal and thermodynamic models. It should be noted intelligent models, such as a vector machine, an artificial neural network, in recent years are increasingly used for modeling various parameters and properties in the oil and chemical industries. However, these models are a black box and cannot provide a clear link between the output and input parameters of the model. In the past few years, models based on the Cubic Plus EoS Association (CPA EoS) and Statistical associating fluid theory (SAFT) have been recognized as promising one for studying asphaltene sediments. However, in the literature, there exist different opinions. Therefore, a systematic study is important for modeling the deposition of asphaltenes. Over the past decades, several different models have been proposed to predict the onset of asphaltenes and the amount of asphaltenes deposited. This paper examines various models that have been proposed to predict asphaltenes deposition under changing thermobaric conditions. A brief summary of various research approaches is presented.The main focus is on the description of the basic assumptions underlying various models, as well as on the ability of the model to correspond to experimental data. The presented models are compared and current modeling trends for forecasting precipitation are shown. This work will help improve understanding of asphaltenes and provide recommendations for the proper study and modeling of asphaltenes in future research.