  The solar atmosphere being magnetic in nature, the understanding of the
structure and evolution of the magnetic field in different regions of the solar
atmosphere has been an important task over the past decades. This task has been
made complicated by the difficulties to measure the magnetic field in the
corona, while it is currently known with a good accuracy in the photosphere
and/or chromosphere. Thus, to determine the coronal magnetic field, a
mathematical method has been developed based on the observed magnetic field.
This is the so-called magnetic field extrapolation technique. This technique
relies on two crucial points: (i) the physical assumption leading to the system
of differential equations to be solved, (ii) the choice and quality of the
associated boundary conditions. In this review, I summarise the physical
assumptions currently in use and the findings at different scales in the solar
atmosphere. I concentrate the discussion on the extrapolation techniques
applied to solar magnetic data and the comparison with observations in a broad
range of wavelengths (from hard X-rays to radio emission).
