  The figure of the Sun reflects its inner structure and dynamics, influencing
also the perihelion precession of close orbiting bodies, like Mercury. To study
the solar figure from ground, the deformation on the solar image induced by the
atmosphere has to be known up to one part over a million, and this is done
through differential refraction models: a historical review of them is drafted.
The solar oblateness has been investigated in order to validate alternative
theories to General Relativity and to understand the internal dynamics of our
star. The solar figure should possess only micro departures from sphericity
according to the standard stellar structure theory and helioseismology data,
though variations along the cycle has been observed. Ground-based and satellite
data show contrasting observational results. The oblateness measured onboard
RHESSI satellite, the one of SDS onboard a stratospheric ballon and that one of
the Astrolabe of Rio de Janeiro are presented with their implications in
classical and relativistic gravitation. The perspectives offered by the
reflecting heliometer in the future measurement of the oblateness are depicted.
