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The history and present state of large-scale magnetohydrodynamic (MHD)modeling of the solar corona and the solar wind with steady or quasi-steadycoronal physics is reviewed. We put the evolution of ideas leading to therecognition of the existence of an expanding solar atmosphere into historicalcontext. The development and main features of the first generation of globalcorona and solar wind models are described in detail. This historicalperspective is also applied to the present suite of global corona and solarwind models. We discuss the evolution of new ideas and their implementationinto numerical simulation codes. We point out the scientific and computationalchallenges facing these models and discuss the ways various groups tried toovercome these challenges. Next, we discuss the latest, state-of-the art modelsand point to the expected next steps in modeling the corona and theinterplanetary medium.

Extended MHD modeling of the steady solar corona and the solar wind