CaCu3Ti4O12 (CCTO) was prepared by solid-state reaction and identified by X-ray diffractometry. The evolution of the microstructure was observed by scanning electron microscopy (SEM). It was found that discontinuous grain growth developed during sintering, and large abnormal grains played a very significant role in the dielectric behavior. Cu ions segregated to the boundaries and CuO located at the triple-point sites of the abnormal large grains were observed by electron energy loss and energy-dispersive X-ray spectroscopy, respectively. Moreover, two kinds of morphologies, i.e., terraces with ledges and bump domains, were discovered inside the grains under the thermal etching conditions at 960degreesC for 72 min, which solves the contradiction related to the interpretation of the giant dielectric response between ceramic and single-crystal CCTO. Complex impedance spectroscopy was used to analyze the conductivity of ceramic CCTO, which suggests that it consists of conducting domains with two kinds of insulating barrier layers of domain and grain boundaries. The insulating domain and grain boundaries were attributed to orderly arranged dislocations and segregation of Cu ions, respectively. The conduction of CCTO was found to be related to the porosity, the grain size, and the thickness of the insulating boundary layers. For a sample sintered at 1065degreesC for 3 h, the anomalously low resistivity and temperature-dependent dielectric constant were due to the fact that domain boundaries were not substantially formed. The possible reasons for the development of barrier layers and the variation of the dielectric constant with the sintering time are discussed. A barrier-layer model with dielectric response based on the Maxwell-Wagner type of relaxation for ceramic CCTO is proposed. Two kinds of dielectric responses occur, depending on the microstructure: they are dominated by the domain and domain boundary and by the grain and grain boundary for large grains and fine grains, respectively.