Abstract: Neutron stars can have magnetic fields of 10^12 G and more. If these objects are located in a binary system with a normal star, accretion of
matter from that star leads to the formation of a X-ray binary. Due to the strong magnetic field, a X-ray pulsar is formed where matter falls along the magnetic field lines onto the magnetic poles of the neutron star. Here, the kinetic energy of the material is converted into photons as it is slowed down from 0.3c to 0c in an accretion column that has a foot print of only 1km^2. The emission from this accretion column allows us to study the behavior of material in very strong magnetic fields, where the motion of electrons around the magnetic field lines is quantized into Landau levels. This quantization leads to absorption lines whose energy depends on the local magnetic field and therefore allows us to measure directly the local magnetic field. In this talk I will discuss the physics of the accretion flow through such magnetospheres and show results from new models for the structure of the accretion column and formation of the cyclotron lines.