In this talk we sketch the basic ideas and methods of a series of papers of Yann Brenier, Norbert Mauser, Marjolaine Puel and Laure Saint-Raymond. We consider asymptotic limits of the (relativistic) Vlasov-Maxwell system with different scalings concerning the magnetic field. The combined “quasi-neutral” and non-relativistic limits thus lead to two different limit systems. In the case when we keep the magnetic field in the non-relativistic limit, we obtain the so-called electron magnetohydrodynamics equations. Otherwise we obtain the incompressible Euler equations with no more magnetic field left. A key tool of the proofs is the method of modulated energy.