We have been studying the (001) surface of WO₃ as a prototype system for understanding how the local structure of a catalytic site on an oxide surface determines its catalytic activity and function. When a freshly cleaved sample is placed into the vacuum chamber (a,b) large terraces are seen but when one looks at high resolution, one sees an atomically rough surface. Heating the sample in 3x10^-5 torr of oxygen for several hours causes the interesting long-range superstructure shown in (c) and (d) to form. We attribute this structure to an ordered array of W₆O₁₈ clusters. Further heating under the same conditions produces the smooth surface shown in (e). Zooming in on the terraces reveals the c(2x2) structure expected for a "fully oxidized" WO₃ surface. This c(2x2) structure consists of an ordered array of oxygen atoms on the surface which appear as the bright spots in the image. Interestingly, if the oxygen pressure is increased during annealing the surface returns to its original rough state; then decreasing the oxygen pressure causes the c(2x2) structure to reappear. Thus the fully oxidized surface is produced by reduction! This contradictory result can be explained in terms of bulk oxidation and reduction.