Konstantin Herbst, Lennart R. Baalmann, Andrei Bykov, N. Eugene Engelbrecht, Stefan E. S. Ferreira, Vladislav V. Izmodenov, Sergey D. Korolkov, Ksenia P. Levenfish, Jeffrey L. Linsky, Dominique M. -A. Meyer, Klaus Scherer, R. Du Toit Strauss

• Thanks to dedicated long-term missions like Voyager and GOES over the past 50 years, much insight has been gained on the activity of our Sun, the solar wind, its interaction with the interstellar medium, and, thus, about the formation, the evolution, and the structure of the heliosphere. Additionally, with the help of multi-wavelength observations by the Hubble Space Telescope, Kepler, and TESS, we not only were able to detect a variety of extrasolar planets and exomoons but also to study the characteristics of their host stars, and thus became aware that other stars drive bow shocks and astrospheres. Although features like, e.g., stellar winds, could not be measured directly, over the past years several techniques have been developed allowing us to indirectly derive properties like stellar mass-loss rates and stellar wind speeds, information that can be used as direct input to existing astrospheric modeling codes. In this review, the astrospheric modeling efforts of various stars will be presented. Starting with the heliosphere as aThanks to dedicated long-term missions like Voyager and GOES over the past 50 years, much insight has been gained on the activity of our Sun, the solar wind, its interaction with the interstellar medium, and, thus, about the formation, the evolution, and the structure of the heliosphere. Additionally, with the help of multi-wavelength observations by the Hubble Space Telescope, Kepler, and TESS, we not only were able to detect a variety of extrasolar planets and exomoons but also to study the characteristics of their host stars, and thus became aware that other stars drive bow shocks and astrospheres. Although features like, e.g., stellar winds, could not be measured directly, over the past years several techniques have been developed allowing us to indirectly derive properties like stellar mass-loss rates and stellar wind speeds, information that can be used as direct input to existing astrospheric modeling codes. In this review, the astrospheric modeling efforts of various stars will be presented. Starting with the heliosphere as a benchmark of astrospheric studies, investigating the paleo-heliospheric changes and the Balmer H alpha projections to 1 pc, we investigate the surroundings of cool and hot stars, but also of more exotic objects like neutron stars. While pulsar wind nebulae (PWNs) might be a source of high-energy galactic cosmic rays (GCRs), the astrospheric environments of cool and hot stars form a natural shield against GCRs. Their modulation within these astrospheres, and the possible impact of turbulence, are also addressed. This review shows that all of the presented modeling efforts are in excellent agreement with currently available observations.…