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The theoretical modeling of the spectral energy distribution of accretion powered X-ray pulsars allows us to test our understanding of the fundamental phenomena occurring in extremely strong magnetic and gravitational fields. At high accretion rates onto the neutron star, the radiative shocks form extensive accretion columns, where the falling plasma is gradually decelerated, producing X-rays. At sufficiently low accretion rates, the physics of accretion is simplified. The tenuous accretion flow captured by the strong magnetic field of the neutron star is insufficient to form an accretion column. Instead, the plasma falls freely onto the poles of the neutron star, and the final stopping by Coulomb interactions occurs only within the thin layer of the neutron star atmosphere. The thermal X-ray emission from the neutron star surface is strongly polarized in the atmosphere, due to magnetized plasma effects and vacuum birefringence. Moreover, its propagation is highly anisotropic and affected by Compton scattering, cyclotron, and free-free emission and absorption, which become resonant processes in the presence of a strong magnetic field. In this talk, I will concentrate on the physical picture of plasma braking by Coulomb collisions, the structure of the Coulomb heated atmospheres, and the formation processes of the polarized radiation from the polar cap of the neutron star.