The structure of the (001) surface of monoclinic gamma -WO3 was characterized using scanning tunneling microscopy (STM), Auger electron spectroscopy (AES), and low-energy electron diffraction (LEED). The surface structure depended strongly on preparation conditions. Oxidizing by heating in O-2 removed carbonaceous impurities and resulted in large atomically rough terraces. Subsequent heating in lower O-2 pressures led to metastable superstructures and c(2X2) terraces. Continued heating progressively reduced the surface, resulting in a series of reconstructions. Each could be explained in terms of ordered oxygen vacancies. First, regions of a c(2X2) reconstruction grew. This structure corresponds to a WO2 plane in which half the W6+ sites are covered by terminal O. Since all the W atoms are in a 6+ oxidation state, this surface is considered "fully oxidized." Certain STM images of the c(2x2) terraces revealed a pseudo-primitive-(2x2) periodicity that can be related to the monoclinic distortion from cubic symmetry. It is shown that the distortion is always present but the ability to detect it depends on the tip. The distortion also caused twinning that lead to spot splitting in LEED patterns. The splitting disappeared on heating to 785 K when the bulk converted to orthorhombic symmetry. Continued reduction produced areas with (2X2), (6X2), and c(4x2) periodicities. These reconstructions are formed when further terminal O is removed, and half the total W sites are reduced to W5+. Sputtering and ultrahigh vacuum annealing also reduced the surface, ultimately leading to "fully reduced" (I X 1) terraces with no terminal oxygen and only W5+ surface cations. These structural transformations were reversible: at any stage during reduction. heating in greater than or equal to 10(-4) Torr Of O-2 reoxidized the surface, regenerating the original rough morphology.