The Magellanic Clouds are surrounded by an extended network of gaseous structures. Chief among these is the Magellanic Stream, an interwoven tail of filaments trailing the Clouds in their orbit around the Milky Way. When considered in tandem with its Leading Arm, the Stream stretches over 200° on the sky. The Stream is thought to represent the result of tidal interactions between the Clouds and ram-pressure forces exerted by the Galactic corona, and its kinematic properties reflect the dynamical history of the pair of dwarf galaxies closest to the Milky Way. The Stream is a benchmark for hydrodynamical simulations of accreting gas and cloud/corona interactions. If the Stream survives these interactions and arrives safely in the Galactic disk, its cargo of over a billion solar masses of gas has the potential to maintain or elevate the Galactic star-formation rate. I review the current state of knowledge of the Stream, physical conditions, origin, and fate. I also review the dynamics of the Magellanic System, including the proper motions and orbital history of the Large and Small Magellanic Clouds, the first-passage and second-passage scenarios, and the evidence for a Magellanic Group of galaxies.