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In this review, I focus on the structure and evolution of the coronalmagnetic fields modelled from observations. The development of instrumentsmeasuring the photospheric and chromospheric magnetic fields with a highspatial and time resolutions allows us to improve the modeling of the coronalfields based on extrapolation and evolution techniques. In particular, I detailthe advance modelling of quiet-Sun areas, active regions and full-discevolution. I discuss the structure of coronal magnetic features such asfilaments, sigmoids and coronal loops as well as their time evolution andinstability. The complexity of the coronal field and the origin of open fluxare also investigated in these different areas. Finally I discuss the futureimprovements in terms of instruments and models required to understand betterthe coronal field.

3D structure of the outer atmosphere: combining models and observations