Polyconjugated polymers resemble inorganic semiconductors phenomenologically inasmuch as their optical gap is in the visible or near infrared and their conductiveity can be increased by several orders of magnitude by doping. However, the models describing the polymers differ from those for conventional semiconductors due to the polymers' quasi-one-dimensional structure. This text presents the various models of -conjugated polymers and the computational methods used to derive the experimentally measurable quantities. The electrical, optical and magnetic properties are described and interpretations of the experimental results are critically reviewed. Emphasis is placed on phenomena involving solitons, polarons, bipolarons, and the relative importance of the electron-phonon and electron-electron interaction. The discussion ranges from well-understood properties to those that still lack a satisfactory explanation.