The central half kiloparsec region of our Galaxy harbors a variety of phenomena unique to the central environment. This review discusses the observed structure and activity of the interstellar medium in this region in terms of its inevitable inflow toward the center of the Galactic gravitational potential well. A number of dissipative processes lead to a strong concentration of gas into a ``Central Molecular Zone'' of about 200-pc radius, in which the molecular medium is characterized by large densities, large velocity dispersions, high temperatures, and apparently strong magnetic fields. The physical state of the gas and the resultant star formation processes occuring in this environment are therefore quite unlike those occuring in the large-scale disk. Gas not consumed by star formation either enters a hot x-ray emitting halo and is lost as a thermally-driven galactic wind, or continues moving inward, probably discontinuously, through the domain of the few parsec-sized circumnuclear disk, and eventually into the central parsec. There, the central radio source SgrA^* currently accepts only a tiny fraction of the inflowing material, likely as a result of a limit cycle wherein the continual inflow of matter provokes star formation, which in turn can temporarily halt the inflow via mass-outflow winds.