  This article proposes a review of the analysis of the system of
magnetohydrodynamics (MHD). First, we give an account of the modelling
asumptions. Then, the results of existence of weak solutions, using the notion
of renormalized solutions. Then, existence of strong solutions in the
neighbourhood of equilibrium states is reviewed, in particular with the method
of Kawashima and Shizuta. Finally, the special case of dimension one is
highlighted : the use of Lagrangian coordinates gives a simpler system, which
is solved by standard techniques.
