There is a broad consensus that electrification holds the key to realizing a decarbonizing society. Even so, the increasing power densification in electronics (high heat flux) and battery systems (high C-Rates) necessitates the demonstration and scale-up of innovative and robust thermal management technologies. Most electronics and electric vehicle operating environments are transient, thereby demanding the need to have a paradigm shift in our approach to thermal management. The transient load is often a high peak way above the average power, and hence a cooling technology based on peak power or heat load will more often than not be sub-optimal and economically not prudent. Thermal management using phase change materials (PCMs) is a promising candidate solution for electronics and batteries, where the PCM offers the ability to store or release the latent heat of the material during the power spikes. Strategies for PCM development have generally focused on augmenting the thermal conductivity of the PCM, which often is abysmally low. This keynote paper will walk the audience through the evolution of the PCM-based heat sink technology, the current state of the art, and prospects. For the most part, the keynote is based on the work of the author's research group and several recent publications from our laboratory. Without much deviation from "the big picture," the paper's focus is also dedicated to numerous intricate details of today's growing power demands in real-time applications, which can significantly affect the design of a PCM-based heat sink and are frequently overlooked. The second part of this paper presents a few candidate thermal conductivity enhancement techniques in PCMs. The outcome of nearly a fifteen-year-old research from our research group on novel thermal conductivity enhancers (TCEs) in the form of metal foams, fins, heat pipes, expanded graphite (EG), and metal matrix to mitigate the poor thermal conductivity of a PCM will be discussed and highlighted. A significant part of the objective of this paper is also to showcase that the figure of merit to evaluate a PCM-based composite performance has evolved in time and continues to be redefined even today. The final part of the paper will highlight the recent contributions to the thermal management of Lithium-ion batteries, including the introduction of PCM and pin fin designs. Ultimately, what is now urgently required is readily available guidelines to quickly arrive at the optimal design (including choice of PCM, size, weight, and geometry) of PCM heat sink for a very specific power intense application. This paper will provide insights into design and optimization guidelines for the future PCM-based composite heat sinks design to address this requirement. Also, a qualitative comparison between various TCEs and PCMs from our own work has been summarized. The paper will conclude by pointing out potential future "thermal threats" posed to researchers in this field, which must be gracefully and steadfastly resolved to sustain the technological progress of human civilization.