Composite cables suitable for use in conjunction with wellbore tools. One cable may include a polymer composite that includes dopants dispersed in a polymer matrix and continuous fibers extending along an axial length of the cable through the polymer matrix, wherein the cable is characterized by at least one of the following: (1) at least a portion of the cable having a density greater than about 2 g/cm3, wherein at least some of the dopants have a density of about 6 g/cm3 or greater, (2) at least a portion of the cable having a density less than about 2 g/cm3, wherein at least some of the dopants have a density of about 0.9 g/cm3 or less, (3) at least some of the dopants are ferromagnetic, or (4) at least some of the dopants are hydrogen getters.