This paper reviews models of helical cable behavior with an emphasis on recent models that study internal cable damping. Cable models are categorized into three major classes consisting of thin rod models, semicontinuous models, and beam models. Research on cable vibration damping resulting from internal factors is investigated and related, with conclusions supported by multiple bodies of work highlighted and inconsistencies that may require further study noted. Internal damping mechanisms due to interwire friction, variable bending stiffness, and internal and viscoelastic dissipation are explored with specific damping terms presented for the various models. Damping through inclusion of friction forces, viscoelastic shear effects, or bending stiffness as a function of cable curvature and wire properties must be included to produce a realistic cable model.