Abstract: Accreting neutron star X-ray binaries represent some of the most extreme environments in the Universe, with gravitational and magnetic fields trillions of times stronger than those found on Earth. In these binary systems, the accretion disk is truncated at the pulsar's magnetosphere where the magnetic pressure exceeds the disk ram pressure. The magnetic field funnels gas along field lines and directly onto the pulsar's magnetic poles, forming structures known as magnetized accretion streams. While theoretical models can predict accretion stream structures, observations are needed to constrain these models and investigate the behavior of matter in these extreme environments. My dissertation provides observational constraints on magnetic accretion streams by probing their structure and kinematics. This thesis primarily makes use of carefully timed X-ray observations that span a complete superorbital cycle within three sources thought to contain warped, precessing inner accretion disks: LMC X-4, SMC X-1, and Her X-1. Using broad-band X-ray coverage to disentangle the observational signatures of the pulsar from the accretion disk, I find that the spectral and pulse profile shapes are periodic with superorbital phase, which is consistent with a precessing inner disk. I used phase-resolved spectroscopy and X-ray tomography to model the geometry of the inner accretion disk, and find my model is capable of reproducing observed changes in pulse profile shape and phase. This thesis also uses X-ray spectral and timing analyses to investigate flaring and transient phenomena in the X-ray binaries LMC X-4 and SAX J2103.5+4545. I discovered pulsation transience in LMC X-4 in association with accretion flares, which suggests changes in the emission geometry as the source undergoes super-Eddington accretion that make LMC X-4 a unique analogue to ultraluminous X-ray pulsars. I also found evidence for a faint, phase-dependent absorption feature in SAX J2103 which, if caused by cyclotron resonance scattering, would indicate that this source has one of the lowest known magnetic fields among X-ray pulsars. My work provides a comprehensive observational view of pulsar magnetic accretion disk structure.