ABSTRACT: Measurements of the linear polarization of far-infrared and submillimeter thermal emission from interstellar dust grains provide information on the configuration of the magnetic field lines that thread molecular clouds. During the last ten years, far-infrared and/or submillimeter polarization has been measured for six distinct regions within the Galactic Center. We compare recent results, including the first detection of submillimeter polarization from clouds in Sgr A, with earlier work, including far-infrared polarimetry of Sgr B2, the 3-pc circumnuclear disk, and the arched filaments. We suggest that the data indicate: (1) a globally azimuthal field beyond a Galactocentric radius of 50 pc, and (2) a more complicated geometry inside 50 pc radius, where we see magnetic fields (in cool regions) that appear to be nearly orthogonal to the Galactic plane. We also show that the expansion of Sgr A(East) has left a clear imprint upon the magnetic field. Finally, we discuss the implications for the magnetic accretion disk model that has been applied to the 3-pc circumnuclear disk.