Conducting organic polymers (COPs) became an active field of research after it was discovered how thin films rather than insoluble infusible powders can be produced. The combination of the properties of plastics with those of semiconductors opened the research field of organic electronics. COPs share many electronic properties with inorganic semiconductors, but there are also major differences, e.g., the nature of the charge carriers and the amount of the exciton binding energy. Theoretical analysis has been used to interpret experimental observations early on. The polaron model that was developed from one-electron theories is still the most widely used concept. In the 1990s, time-dependent density functional theory (TDDFT) became available for routine calculations. Using TDDFT, electronic states of long oligomers can be calculated. Now UV spectra of neutral and oxidized or reduced species can be compared with in situ UV spectra recorded during doping. Likewise states of cations can be used to model photoelectron spectra. Analysis of states has resolved several puzzles which cannot be understood with the polaron model, e.g., the origin of the dual absorption band of green polymers and the origin of a 'vestigial neutral band' upon doping of long oligomers. DFT calculations also established that defect localization is not crucial for spectral changes observed during doping and that there are no bound bipolarons in COPs.