The electronic structure of the charge carrier in one of the most commonly used semiconducting polymers (poly(3-hexylthiophene (P3HT)) is described using a combination of classical and quantum chemical methods. It is shown that the carriers are localized in correspondence with long-lived traps which are present also in the crystalline phase of the polymer. The existence of activated transport for very ordered polymer phases (regardless of the strength of the polaron formation energy) is explained, and the trapped states, postulated by many phenomenological models, are described for the first time with chemical detail. It is shown that computational chemistry methods can be used to fill the gap between phenomenological descriptions of charge transport in polymers and microscopic descriptions of the individual quantum dynamic processes.