  Sunspots are of basic interest in the study of the Sun. Their relevance
ranges from them being an activity indicator of magnetic fields to being the
place where coronal mass ejections and flares erupt. They are therefore also an
important ingredient of space weather. Their formation, however, is still an
unresolved problem in solar physics. Observations utilize just 2D surface
information near the spot, but it is debatable how to infer deep structures and
properties from local helioseismology. For a long time, it was believed that
flux tubes rising from the bottom of the convection zone are the origin of the
bipolar sunspot structure seen on the solar surface. However, this theory has
been challenged, in particular recently by new surface observation,
helioseismic inversions, and numerical models of convective dynamos. In this
article we discuss another theoretical approach to the formation of sunspots:
the negative effective magnetic pressure instability. This is a large-scale
instability, in which the total (kinetic plus magnetic) turbulent pressure can
be suppressed in the presence of a weak large-scale magnetic field, leading to
a converging downflow, which eventually concentrates the magnetic field within
it. Numerical simulations of forced stratified turbulence have been able to
produce strong super-equipartition flux concentrations, similar to sunspots at
the solar surface. In this framework, sunspots would only form close to the
surface due to the instability constraints on stratification and rotation.
Additionally, we present some ideas from local helioseismology, where we plan
to use the Hankel analysis to study the pre-emergence phase of a sunspot and to
constrain its deep structure and formation mechanism.
