Extending for over 200 degrees across the sky, the Magellanic Stream together with its Leading Arm is the most spectacular example of a gaseous stream in the local Universe. The Stream is an interwoven tail of filaments trailing the Magellanic Clouds as they orbit the Milky Way. Thought to be created by tidal forces, ram pressure, and halo interactions, the Stream is a benchmark for dynamical models of the Magellanic System, a case study for gas accretion and dwarf-galaxy accretion onto galaxies, a probe of the outer halo, and the bearer of more gas mass than all other Galactic high velocity clouds combined. If it survives to reach the Galactic disk, it may maintain or even elevate the Galactic star-formation rate. In this white paper, we emphasize the Streams importance for many areas of Galactic astronomy, summarize key unanswered questions, and identify future observations and simulations needed to resolve them. We stress the importance of ultraviolet, optical, and radio spectroscopy, and the need for computational models that capture full particle and radiation treatments within an MHD environment.