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Modeling of the global heliosphere is essentially important for interpretation of the relevant space experiments both inside the heliosphere and inside the SW/LISM interstellar medium. Modern models of the SW/LISM interactions are 3D multi-component kinetic-MHD models that take into account effects of both the solar wind and local interstellar plasma (including solar wind alpha-particles and interstellar helium), both the heliospheric and interstellar magnetic fields, interstellar hydrogen atoms and pickup protons. In addition, the models may take into account the latitudinal dependence of the solar wind and time-variations. In this presentation I will make an attempt to critivally review current status in the modeling of the SW/LISM interactions and discuss relevance of existing models for interpretation of available observational data.