Additive manufacturing is a cutting-edge process that enables the creation and development of complex shapes, opening new avenues for advanced heat sink designs that maximize heat transfer while minimizing pressure drop. This review provides an overview of recent results and insights from global researchers on the additive manufacturing of microchannel heat sinks. It discusses various novel microchannel heat sink types fabricated using additive manufacturing and the complexities involved in their fabrication. Additionally, the review explores geometric configurations, the application of computational optimization methods, and the impact of surface roughness on heat transfer and pressure drop. The primary focus is on the fundamental advantages of additive manufacturing in addressing complex heat transfer designs. However, the review also highlights limitations restricting its benefits in specific applications, such as material handling and availability. This review identifies future challenges for creating novel heat sinks with complex geometries and opportunities for advancements in heat transfer technology.