The atomic and electronic structures of 60• glide perfect and 30• /90• 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 quadruplyperiodic (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• perfect and 30• partials or the DP reconstruction for the Cd-core 90• partial, results in semiconducting character, as opposed to the metallic character of the SP dislocation cores. Dislocation-induced defect states for the 60• 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• Cd-/Te-core partial dislocations. In addition to the intra-core charge modulation within each QP core, the possibility of inter-core 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.