The anomalous low temperature transport properties of highly doped conjugated polymers are considered. It is concluded that the behavior observed is in particular related to glassy properties of the polymer structure. The two-level-system (TLS) model and the more general soft-potential model are applied to explain the behavior of the conductivity at temperatures from several mK up to 50 to 70 K. The negative temperature resistance coefficient observed at low temperatures is attributed to weak localization which is at higher temperatures suppressed by a strong inelastic scattering of electrons by low energy vibrational excitations typical for glasses.