In this thesis, the properties of the circumstellar environment of the high-mass X-ray binary system SMC X- 1/Sk 160 are explored using observational data from several satellite X-ray observatories. First, we have investigated the cause of the quasiperiodic ~60 day high-state low-state X-ray flux variation, previously suggested, and now clearly evident in extensive BATSE and RXTE monitoring data. Data from short-term pointed observations with the Ginga, ROSAT, ASCA, and RXTE observatories, show that while the uneclipsed flux varies by as much as a factor of 20 between high and low states, the eclipsed flux consists of approximately the same flux of reprocessed radiation in both states. From this we conclude that the high-low cycle is due to a quasi-periodic occultation of the source, most likely by a precessing tilted accretion disk around the neutron star. Next, we investigate the composition and distribution of the wind of Sk 160, the supergiant companion of the X-ray star SMC X-1, by comparing an X-ray spectrum of the source, obtained with the ASCA observatory during an eclipse with the computed spectra of reprocessed radiation from circumstellar matter with various density distributions. We show that the metal abundance in the wind of SMC X-1 is no greater than a few tenths of solar, as has been determined for other objects in the Magellanic Clouds. We also show that the observed spectrum is not consistent with the density distributions of circumstellar matter of the spherically symmetric form derived for line-driven winds, nor the density distribution from a hydrodynamic simulation of the X-ray perturbed and line-driven wind by Blondin & Woo (1995). Essential properties of a density distribution that would yield agreement with the observed spectrum are defined. Finally, we discuss prospects for future studies of this kind based on high-resolution spectroscopy data expected from the AXAF mission. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)