The interaction of the solar wind with the interstellar medium is complicated by the presence of a substantial neutral component, interstellar hydrogen. The self-consistent inclusion of neutral hydrogen (and other heavier atoms) requires that models include the effects of charge exchange and scattering properly. With the crossing of the heliospheric termination shock by the Voyager 1 and 2 spacecraft, understanding the outer heliosphere and the heliospheric boundaries has become a topic of great interest. IBEX is now returning observations of Energetic Neutral Atoms (ENAs) created in the solar wind – interstellar medium boundary regions, and these are providing both new insights and new challenges to our understanding of the physics in this complex region. We will describe the status of modeling the solar wind-local interstellar medium interaction, its relationship to Voyager 1 and 2 and IBEX and other remote observations, and the implications for the interaction of stellar winds with their local interstellar environments. The discovery of the hydrogen wall around our heliosphere and other “astrospheres” will be discussed.