  In this review, our present day understanding of the Sun's global
photospheric and coronal magnetic fields is discussed from both observational
and theoretical viewpoints. Firstly, the large-scale properties of photospheric
magnetic fields are described, along with recent advances in photospheric
magnetic flux transport models. Following this, the wide variety of theoretical
models used to simulate global coronal magnetic fields are described. From
this, the combined application of both magnetic flux transport simulations and
coronal modeling techniques to describe the phenomena of coronal holes, the
Sun's open magnetic flux and the hemispheric pattern of solar filaments is
discussed. Finally, recent advances in non-eruptive global MHD models are
described. While the review focuses mainly on solar magnetic fields, recent
advances in measuring and modeling stellar magnetic fields are described where
appropriate. In the final section key areas of future research are identified.
