Phase-change materials, also well known as the Chalcogenide alloy, have received considerable attention during last two decades owing to its widespread applications in the field of the electrical storage market such as phase-change random access memory and phase-change probe memory. In addition to the storage devices, its unique electrical properties that can be dynamically tunable with respect to the electrical excitations lead to numerous novel applications represented by memristor and memristor-based neuromorphic electrical circuits. These emerging applications undoubtedly allows for a further exploitation of the potential of phase-change materials, and thus makes it advantageous over other storage medium like ferroelectric and magnetic materials. In order to help researchers understand the role of phase-change materials in these novel applications as well as their importance for citizen's daily life, a comprehensive review that not only covers the traditional storage applications, but also the applications on these exotic devices becomes imperative. In this review, the chemical structure of phase-change materials and their remarkable electrical properties are first reviewed, followed by an introduction of their applications on the storage fields. The physical principles of various emerging electrical devices using phase-change materials are subsequently overviewed in association with their state-of-the-art progress. The prospect of phase-change materials for the future non-volatile electrical applications that are yet to be unraveled is finally envisaged.