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.
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