Phase-change memory (PCM) is an emerging non-volatile memory technology that has recently been commercialized as storage-class memory in a computer system. PCM is also being explored for non-von Neumann computing such as in-memory computing and neuromorphic computing. Although the device physics related to the operation of PCM have been widely studied since its discovery in the 1960s, there are still several open questions relating to their electrical, thermal, and structural dynamics. In this article, we provide an overview of the current understanding of the main PCM device physics that underlie the read and write operations. We present both experimental characterization of the various properties investigated in nanoscale PCM devices as well as physics-based modeling efforts. Finally, we provide an outlook on some remaining open questions and possible future research directions.