Models of polymeric methyltrioxorhenium (poly-MTO), recently synthesized by Herrmann et al., were investigated by the extended Huckel approximate molecular orbital method. The bandstructure of poly-MTO resembles that of ReO3, but important differences arise from the two-dimensional nature of poly-MTO. The conductivity of poly-MTO can be attributed to occasional demethylation and to the inclusion of extra hydrogen in the lattice. Due to the polymeric nature of poly-MTO, rhenium atoms missing methyl groups are found to be oxidized rather than reduced. A variety of sites for the inclusion of hydrogen in poly-MTO are explored. The H is protonic and, to the extent it is there, provides further reduction of the Re and weakens locally some of the ReO bonds.