  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.
