Gas dynamic structure of the heliosphere is determined by the solar wind interaction with the supersonic flow of the partially ionized local interstellar medium (LISM). Historical review of this problem investigation is given here. General picture of the considered flow, a mathematical formulation of the gas‐kinetic model and its basic results are presented. It is shown that for forecasting of future experimental results it is necessary to construct the models with physically and mathematically correct theoretical basis. Examples of experimental data which can be explained on the basis of theoretical predictions are given. Results of the Ohm’s law analysis for partially ionized hydrogen gas show that a conception of the magnetic field freezing in plasma for the problem of the solar wind interaction with the magnetized LISM flow can be not correct if to take into account the processes of the resonance charge exchange. © 2003 American Institute of Physics