The atomic and electronic structures of ${60}^{\ensuremath{\circ}}$ glide perfect and ${30}^{\ensuremath{\circ}}/{90}^{\ensuremath{\circ}}$ glide partial dislocations in CdTe are studied using combined semi-empirical and density functional theory calculations. The calculations predict that the dislocation cores tend to undergo significant reconstructions along the dislocation lines from the singly-periodic (SP) structures, yielding either doubly-periodic (DP) ordering by forming a dimer or quadruply-periodic (QP) ordering by alternating a dimer and a missing dimer. Charge modulation along the dislocation line, accompanied by the QP reconstruction for the Cd-/Te-core ${60}^{\ensuremath{\circ}}$ perfect and ${30}^{\ensuremath{\circ}}$ partials or the DP reconstruction for the Cd-core ${90}^{\ensuremath{\circ}}$ partial, results in semiconducting character, as opposed to the metallic character of the SP dislocation cores. Dislocation-induced defect states for the ${60}^{\ensuremath{\circ}}$ Cd-/Te-core are located relatively close to the band edges, whereas the defect states lie in the middle of the band gap for the ${30}^{\ensuremath{\circ}}$ Cd-/Te-core partial dislocations. In addition to the intracore charge modulation within each QP core, the possibility of intercore charge transfer between two different dislocation cores when they are paired together in the same system is discussed. The analysis of the electronic structures reveals the potential role of the dislocations on charge transport in CdTe, particularly in terms of charge trapping and recombination.