Demand for memory devices is continuously increased by consumer electronics and data storage needs. Phase-change memory (PCM) is appealing for future memory systems with key features including the opportunity for sub-10 nm low-power devices. PCM technology relies on so-called threshold switching behavior, a sudden and large change in the resistivity of the material that may or may not be accompanied by phase change (e.g. crystallization) depending on the material chosen. In the present talk, carrier transport is analyzed in the framework of trap-limited conduction, which has been derived following a new approach similar to that of the hydrodynamic model in standard semiconductor theory. Threshold switching has been interpreted by means of the well-established and solid physical background of hot carriers under non-uniform electric fields. The model has proven to successfully reproduce the experimental electrical characteristics of memory devices and can be exploited to predict device performance, including material, scalability, and reliability issues.