Poly(3,4-ethylenedioxythiophene) (PEDOT) is the prototypical conjugated polymer used in the doped state as the hole injection/transport layer in organic (opto)electronic devices. Numerous experimental studies have been successful only in drawing a partial microscopic picture of PEDOT due to its complex morphology, which has also hampered application of theoretical approaches. Using density functional theory methods, combined with refined structural models built upon crystallographic data of PEDOT and other substituted polythiophenes, our work seeks to establish a comprehensive understanding of the electronic and geometric structures of PEDOT, as an isolated chain and in the pristine and doped bulk phases. We find that ethylenedioxy substitution planarizes the polythiophene backbone but the experimentally observed bandgap reduction is caused mainly by a stronger destabilization of the valence band than the conduction band via donor-type substitution. The calculated crystal of pristine PEDOT has a monoclinic lamellar structure consisting of inclined T.-stacks. The impact of interchain interactions on the charge carrier effective masses is greater than that of the ethylenedioxy substitution and leads to the reversal of the relative masses; the electrons are lighter than the holes in the pristine crystal. The small interchain electron effective mass is comparable to the hole effective masses found in high mobility organic crystals. Tosylic acid-doped PEDOT (PEDOT:Tos), which is receiving renewed interest as an anode material to replace indium tin oxide, is calculated to be a two-dimensional-like metal. The PEDOT:Tos crystal is found to have an embedded mirror plane in the tosylate monolayer that is sandwiched between PEDOT stacks, and thus to have twice the size of the unit cell proposed earlier. Doping is seen to remove the intrastack inclination of the PEDOT chains.