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

In this review, I focus on the structure and evolution of the coronal magnetic fields modelled from observations. The development of instruments measuring the photospheric and chromospheric magnetic fields with a high spatial and time resolutions allows us to improve the modeling of the coronal fields based on extrapolation and evolution techniques. In particular, I detail the advance modelling of quiet-Sun areas, active regions and full-disc evolution. I discuss the structure of coronal magnetic features such as filaments, sigmoids and coronal loops as well as their time evolution and instability. The complexity of the coronal field and the origin of open flux are also investigated in these different areas. Finally I discuss the future improvements in terms of instruments and models required to understand better the coronal field.