Neutron stars in binary systems can accrete matter from their companion star via an accretion disk. Some accreting neutron stars alternate between periods of sustained rotational acceleration and deceleration, such that the intervals of positive and negative torque last for weeks or years, but the transition between them occurs suddenly, over just days. The origin of these toque reversals is not understood, because the time dependent transfer of angular momentum between the accretion disk and the neutron star, carried by the infalling matter itself and the magnetic field lines threading the flow, is also not understood. This project investigates the problem of angular momentum transfer between the accretion disk and the stellar magnetosphere. First, we develop a global, non-linear model for the star-disk system, based on an approach by Spruit-Taam, but with an approved description of the disk-magnetosphere coupling. We show that the system can exist in two stable states, corresponding to opposite signs of torque on the star. The torques and transition time scales predicted by our model are consistent with observations. Second, we point out that the viscous torque in the disk-magnetosphere boundary layer, neglected in the Spruit-Taam model, can be much larger than the magnetic torque- an important result for future models. Finally we perform simulations of the Kelvin-Helmhotz instability in the boundary layer between the disk and magnetosphere, using a vortex-in-cell code- the first time that such a code gas been written to study accretion problems. We show that the rate at which material is transported across the boundary layer is suppressed for thin boundary layers, a new result that contradicts the Spruit-Taam model.