In-memory computing (IMC) is an emerging computing paradigm where the physical attributes of memory devices are exploited to compute in place thus obviating the need to shuttle around data between memory and processing units. Phase-change memory, with its well understood device physics, volumetric switching and easy embeddability in a CMOS platform is particularly well suited for IMC. The analog storage enables efficient matrix-vector multiply operations that are key to applications such as deep neural network inference. It has been shown that software-equivalent classification accuracies can be reached with custom training procedures. Recently, a fully integrated PCM-based IMC core was introduced where the PCM array is integrated in 14nm CMOS technology. In this talk, I will give an overview of the state-of-the-art on PCM-based IMC, some of the key challenges and will provide an overview of the research directions aimed at overcoming those challenges.