Electronic structure and optical absorption spectra of poly(3,4-ethyl-enedioxythiophene) (PEDOT) for different oxidation levels were studied using density functional theory (DFT) and time-dependent DFT. It is shown, that the DFT-based predictions for the polaronic and bipolaronic states and the nature of corresponding optical transitions are qualitatively different from the widely used traditional picture based on semi-empirical pre-DFT approaches that still dominate the current literature. On the basis of the results of our calculations, the experimental Vis/NIR absorbance spectroscopy and the electron paramagnetic resonance spectroscopy are re-examined, and a new interpretation of the measured spectra and the spin signal, which is qualitatively different from the traditional interpretation, is provided. The findings and conclusions concerning the nature of polaronic and bipolaronic states, band structure and absorption spectra presented for PEDOT, are generic for a wide class of conducting polymers (such as polythiophenes and their derivatives) that have a similar structure of monomer units.