Kleimann, JensDialynas, KonstantinosFraternale, FedericoGalli, AndréHeerikhuisen, JacobIzmodenov, VladislavKornbleuth, MarcOpher, MeravPogorelov, Nikolai2023-02-132023-02-132022-06-010038-6308https://hdl.handle.net/10289/15534This review summarizes the current state of research aiming at a description of the global heliosphere using both analytical and numerical modeling efforts, particularly in view of the overall plasma/neutral flow and magnetic field structure, and its relation to energetic neutral atoms. Being part of a larger volume on current heliospheric research, it also lays out a number of key concepts and describes several classic, though still relevant early works on the topic. Regarding numerical simulations, emphasis is put on magnetohydrodynamic (MHD), multi-fluid, kinetic-MHD, and hybrid modeling frameworks. Finally, open issues relating to the physical relevance of so-called “croissant” models of the heliosphere, as well as the general (dis)agreement of model predictions with observations are highlighted and critically discussed.application/pdfEnglish© The Author(s) 2022. This work is licensed under a CC BY 4.0 licence.Science & TechnologyPhysical SciencesAstronomy & AstrophysicsHeliosphereAnalyticalNumericalModelingINTERSTELLAR MAGNETIC-FIELDANOMALOUS COSMIC-RAYSLY-ALPHA ABSORPTIONSOLAR-WIND INTERACTIONPICK-UP IONSSELF-CONSISTENT MODELTERMINATION SHOCKLYMAN-ALPHAVOYAGER 2OUTER HELIOSPHEREJournal Article10.1007/s11214-022-00902-61572-9672