The solar system moves through interstellar space populated by three principal particle species: plasma with magnetic field, neutral atoms, and galactic cosmic rays. Their interaction with the solar wind creates what is known as the heliospheric interface, containing two shocks and a tangential discontinuity. The 21st century view of the heliosphere is emerging as a highly dynamic, non‐stationary environment with plasma flows carrying imprints of the solar cycle variations. Instabilities produced by interactions between non‐equilibrium flows add to the complexity and may have important implications for charged particle transport near the heliopause. Proliferation of MHD models brought discoveries of new effects caused by the heliospheric magnetic field geometry and a realization of the importance of the magnitude and direction of the interstellar field on the properties of the bow shock. Finally, cosmic ray evolution in the global heliosphere was found to be a more complex process with a variety of modulation and acceleration sites, including the heliosheath and the heliotail. The role of cosmic rays as a dynamic variable in determining the global structure is now being reassessed. Here we will review the latest theoretical and modeling development and discuss future challenges awaiting the global heliospheric community. © 2004 American Institute of Physics