The Smithsonian Astrophysical Observatory is currently designing and constructing the Submillimeter Array (SMA). This instrument will consist of six 6-m telescopes, which can be moved and reconfigured in four concentric ring-like arrangements with maximum baselines of 500 m. Pending negotiations, the SMA will be sited on Mauna Kea at the 4000 m plateau, adjacent to the existing CSO and JCMT submillimeter telescopes. The goal of the SMA is to provide imaging at sub-arcsecond resolution for the wavelength range of 1.3 mm to 0.35 mm. This instrument will therefore improve the angular resolution achieved with present submillimeter telescopes by more than an order of magnitude. As the cool (10-100 K) dust and gas in the Milky Way and other external systems will radiate principally in the submillimeter wavelengths, we expect the SMA to provide unprecedented resolution and to make fundamental contributions to many different problems including the studies of our solar system, star formation and circumstellar disks, galaxies and molecular cloud structures, quasars and active galactic nuclei, and perhaps even galaxy formation in the early universe.