Carbon fiber polymer-matrix composites are used for high-performance lightweight structures. Since they are conductive, their dielectric behavior has received little attention. The dielectric behavior stems from the interaction of a small fraction of the carriers (mobile electrons) with the atoms, particularly those at interfaces. This interaction results in polarization. The permittivity is high, as predicted theoretically by Jonscher (1999) for high-conductivity materials in general. The first experimental confirmation of the prediction was made by the author (2019). The polarization gives rise to capacitance, which serves to indicate deformation and damage. This means that the structural material senses itself without device incorporation, i.e., self-sensing. Carbon fiber composites are more conductive in the in-plane direction than the through-thickness direction. As a result, the permittivity is much higher in the in-plane direction. Damage causes permittivity decrease. Resistance-based sensing is limited to conductive materials, whereas capacitance-based sensing is applicable to both conductors and nonconductors.