<p>Electronic gadgets have become more powerful and compact depending upon the demand in recent times. These compact devices require high power density and, upon continuous usage, will generate a certain amount of heat. The generated heat, if not dissipated properly, will affect the performance of the component and finally lead to electronic failure. This brings up the need for proper thermal management for the effective performance and durability of the devices. Traditional heatsinks, which have been the ready-to-go solution for effective heat dissipation, are now facing challenges mainly due to the miniaturization of electronic devices where space constraints and power densities are of concern; the limitations of these conventional systems have become evident and developed a new approach such as polymer-based heat sinks. This review deals with the overview of the evolution of thermal management systems, mainly for electronic cooling purposes, from the traditional metallic heatsinks to the cutting-edge development of flexible polymer-based heat sinks. This paper discusses traditional heat sinks and their advances, such as using fin-based heat sinks. It also studies the amalgamation of phase change materials (PCMs), nanomaterials, and flexible substrates, which offer enhanced thermal performance and adaptability to complex geometries. Finally, the review provides a glimpse into future research directions for the development of TES systems for electronic cooling, aiming to inspire further innovation in this critical area.</p>