Terahertz steady-state and time-resolved conductivity and permittivity spectra were measured in 3D graphene networks assembled in free-standing covalently cross-linked graphene aerogels. Investigation of a transition between reduced-graphene oxide and graphene controlled by means of high-temperature annealing allowed us to elucidate the role of defects in the charge carrier transport in the materials. The THz spectra reveal increasing conductivity and decreasing permittivity with frequency. This contrasts with the Drude- or Lorentz-like conductivity typically observed in various 2D graphene samples, suggesting a significant contribution of a relaxational mechanism to the conductivity in 3D graphene percolated networks. The charge transport in the graphene aerogels exhibits an interplay between the carrier hopping among localized states and a Drude contribution of conduction-band carriers. Upon photoexcitation, carriers are injected into the conduction band and their dynamics reveals picosecond lifetime and femtosecond dephasing time. Our findings provide important insight into the charge transport in complex graphene structures.