Phase change memory (PCM) operation relies on a combination of electrical, thermal and structural effects at the nanoscale [1-5]. Under an externally-applied electric field, electrical current flows across the device and cause power dissipation and a consequent increase of local temperature, thus inducing crystallization or melting/amorphization, depending on temperature (hence on voltage and current). The corresponding change of the device resistance can then be sensed by application of a relatively low voltage. Electrical characteristics of the crystalline and amorphous phases thus play a fundamental role in the programming and read behavior of the PCM device. The electrical current-voltage characteristics of the PCM device, for instance, control the read current margin, the programming current, and the energy consumption during memory array operation. To design the driving circuits for generating the voltage pulses for memory program and read, or for selecting the correct select device to allow selection/unselection of memory bits within a crosspoint array, the device characteristics are an essential piece of information. The same applies to sensing circuits aimed at reading the memory state. Finally, the dependence of voltage and currents on the device geometry (e.g., thickness of the active layer, diameter of the bottom electrode) plays a leading role in determining the scaling behavior of the PCM device for various technology nodes. Optimization of PCM device should include a careful consideration of the electrical behavior, in combination to structural properties (melting and crystallization point, activation energy of crystallization, etc.) and thermal characteristics (thermal conductivity, thermal boundary resistances, etc.). This chapter summarizes the fundamental electrical properties of PCM devices in both the amorphous and crystalline states. First, the band structure of crystalline and amorphous phase change materials will be studied based on the analysis of thin films of active materials. Then, the device characteristics in a PCM device including conduction and threshold switching phenomena will be shown. Finally, the effects of non-uniform resistivity, the transient phenomena after switching, and the thermo-electric effects due to the coupling of the temperature distribution with the electrical characteristics will be illustrated.