The structural behavior of GeO2 glass has been investigated up to 64 GPa using results from x-ray absorption spectroscopy in a diamond anvil cell combined with previously reported density measurements. The difference between the nearest Ge-O distances of glassy and rutile-type GeO2 disappears at the Ge-O distance maximum at 20 GPa, indicating completion of the tetrahedral-octahedral transition in GeO2 glass. The mean-square displacement σ(2) of the Ge-O distance in the first Ge-O shell increases progressively to a maximum at 10 GPa, followed by a substantial reduction at higher pressures. The octahedral glass is, as expected, less dense and has a higher compressibility than the corresponding crystalline phase, but the differences in Ge-O distance and density between the glass and the crystals are gradually eliminated over the 20-40 GPa pressure range. Above 40 GPa, GeO2 forms a dense octahedral glass with a compressibility similar to that of the corresponding crystalline phase (α-PbO2 type). The EXAFS and XANES spectra show evidence for subtle changes in the dense glass continuing to occur at these high pressures. The Ge-O bond distance shows little change between 45-64 GPa, and this may reflect a balance between bond shortening and a gradual coordination number increase with compression. The density of the glass is similar to that of the α-PbO2-type phase, but the Ge-O distance is longer and is close to that in the higher-coordination pyrite-type phase which is stable above ∼60 GPa. The density data provide evidence for a possible discontinuity and change in compressibility at 40-45 GPa, but there are no major changes in the corresponding EXAFS spectra. A pyrite-type local structural model for the glass can provide a reasonable fitting to the XAFS spectra at 64 GPa.