In this review, our present day understanding of global magnetic fields on the Sun and other stars has been discussed from both observational and theoretical viewpoints. For the Sun, we now have long-running data sets of global magnetic activity. For other stars, we are just beginning to learn of the wide variety of magnetic morphologies that exist. In terms of theoretical models, recent years have seen a significant advance in global modeling techniques. Global magnetic fields may be modeled under the nonlinear force-free approximation for long periods of time, or for short periods of time using highly detailed MHD models. A key feature of these models is that they have been validated through various comparisons with observations. While our understanding has significantly increased over the last decade, there are several immediate outstanding issues. Five of these are discussed below, where the list is not exhaustive and the order in no way reflects their importance.

- While we have a detailed understanding of the normal magnetic field component on the solar photosphere, the same is not true for the vector field. Between SDO and SOLIS we now have daily full disk vector magnetograms. Analysis of these will gain us an understanding of the emergence and transport of vector fields across the Sun, as well as the origin and evolution of magnetic helicity, a key component in eruptive phenomena. Additionally, vector magnetic field measurements are need not just in strong field regions, but also in weak field regions.
- For theoretical models, regular observations of the vector fields mean that more constraints can be applied to input data of bipole emergences that are used to drive these models. New techniques must be developed for the incorporation of vector data into simulations. Only through this can theory and observations be truly unified.
- A number of inconsistencies with the application of surface flux transport models need to be resolved. These relate to the use of additional decay terms, variations in the rate or profile of meridional flow, and the exact tilt angle applied for new emerging bipoles. Currently various combinations of all of these have been shown (when coupled with different coronal models) to give similar results. It would be useful for the various authors to resolve these issues through comparing results from their codes, driven by the variety of input data sets available. In addition, more constraints on the input data are required from observations.
- While our understanding of stellar magnetic fields has greatly increased, observations are still sporadic. Long term data sets of individual stars across different spectral types are required. From this we may deduce different magnetic flux emergence and transport parameters which are critical for the next generation of dynamo models.
- Global time-dependent MHD models with evolving lower boundary conditions must be developed, to provide a self-consistent model for the evolution and interaction of magnetic fields with plasma.

These issues may be addressed with the current suite of ground and space-based observatories along with developing new theoretical techniques. A key element in achieving this goal is the increasing computing power available both for real-time data reduction and for theoretical modeling. Future revisions of the article will hopefully describe answers to some of these questions. Along with answering these questions, the scope of the review in future revisions will also be increased to include additional topics such as: the connection between the Sun and Heliosphere, observations of coronal and solar prominence magnetic fields, global eruptive models and a fuller discussion of the consequences of observational limitations on the models which directly employ observations.

Living Rev. Solar Phys. 9, (2012), 6
http://www.livingreviews.org/lrsp-2012-6 |
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