Chalcogenide phase-change materials (PCMs), such as Ge-Sb-Te alloys, have shown outstanding properties, which has led to their successful use for a long time in optical memories (DVDs) and, recently, in non-volatile resistive memories. The latter, known as PCM memories or phase-change random access memories (PCRAMs), are the most promising candidates among emerging non-volatile memory (NVM) technologies to replace the current FLASH memories at CMOS technology nodes under 28 nm. Chalcogenide PCMs exhibit fast and reversible phase transformations between crystalline and amorphous states with very different transport and optical properties leading to a unique set of features for PCRAMs, such as fast programming, good cyclability, high scalability, multi-level storage capability, and good data retention. Nevertheless, PCM memory technology has to overcome several challenges to definitively invade the NVM market. In this review paper, we examine the main technological challenges that PCM memory technology must face and we illustrate how new memory architecture, innovative deposition methods, and PCM composition optimization can contribute to further improvements of this technology. In particular, we examine how to lower the programming currents and increase data retention. Scaling down PCM memories for large-scale integration means the incorporation of the PCM into more and more confined structures and raises materials science issues in order to understand interface and size effects on crystallization. Other materials science issues are related to the stability and ageing of the amorphous state of PCMs. The stability of the amorphous phase, which determines data retention in memory devices, can be increased by doping the PCM. Ageing of the amorphous phase leads to a large increase of the resistivity with time (resistance drift), which has up to now hindered the development of ultra-high multi-level storage devices. A review of the current understanding of all these issues is provided from a materials science point of view.