  The physics of brown dwarfs has continuously improved since the discovery of
these astrophysical bodies. The first important developments were devoted to
the description of their mechanical structure, with the derivation of an
appropriate equation of state, and the modelling of their atmosphere
characterised by strong molecular absorption. New challenges are arising with
progress in observational techniques which provide data of unprecedented
accuracy. The goal of this chapter is to describe some of the current
challenges for the theory of brown dwarfs. Those challenges concerns
atmospheric dust and cloud, non-equilibrium atmospheric chemistry, the effect
of rotation and magnetic fields on internal structure and the very early phases
of evolution characterised by accretion processes. The field remains lively as
more and more high quality observational data become available and because of
increasing discoveries of exoplanets. Indeed, many physical properties of giant
exoplanets can be described by the same theory as brown dwarfs, as described in
this chapter.
