Insurgency conflicts pose significant challenges to societies globally. The increase of insurgency conflicts creates a need to understand how insurgencies arise, and to identify societal drivers of insurgencies or effective strategies to counter them. In this paper, we analyze the contributions of computational modeling methods for the analysis of insurgent conflicts. We formalize a specific literature-based analysis framework using the identified key factors and drivers, which enables the evaluation of specific models in this domain. Through a systematic literature search, we identify 64 computational models to apply our framework. We highlight the development and contributions of various methodologies through an in-depth analysis of 13 high-quality models. The evaluation of these computational models revealed promising directions and future topics to design specific simulation models for all identified factors. In addition, our analysis revealed specific pitfalls concerning validity issues for each of the modeling methods.