In this presentation, I will talk about the mechanisms of forming and maintaining a mountain on a neutron star by its magnetic field. In order to do so, I am going to introduce the important equations of magnetohydrodynamics (MHD) that describe this system both in the classical and in the general relativistic paradigms. Then, I will show the numerical solutions of the general relativistic MHD equations governing the system, and compare them with previously obtained Newtonian results in the literature. The comparison will focus on the hydromagnetic structure of the mountains, on the ellipticity of the star and on the process of polar magnetic field burial. Finally, I will trace the implications of these results for the search for continuous gravitational waves.