Spin-transfer torque-based magnetoresistive random access memory (STT-MRAM) is a promising candidate for universal memory that may replace traditional memory forms. It is expected to provide high-speed operation, scalability, low-power dissipation, and high endurance. MRAM switching technology has evolved from the field-induced magnetic switching (FIMS) technique to the spin-transfer torque (STT) switching technique. Additionally, material technology that induces perpendicular magnetic anisotropy (PMA) facilitates low-power operation through the reduction of the switching current density. In this paper, the modeling of magnetic tunnel junctions (MTJs) is reviewed. Modeling methods and models of MTJ characteristics are classified into two groups, macromodels and behavioral models, and the most important characteristics of MTJs, the voltage-dependent MTJ resistance and the switching behavior, are compared. To represent the voltage dependency of MTJ resistance, some models are based on physical mechanisms, such as Landau-Lifshitz-Gilbert (LLG) equation or voltage-dependent conductance. Some behavioral models are constructed by adding fitting parameters or introducing new physical parameters to represent the complex switching behavior of an MTJ over a wide range of input current conditions. Other models that are not based on physical mechanisms are implemented by simply fitting to experimental data.