On-skin wearable systems for biofluid sampling and biomarker sensing can revolutionize the current practices in healthcare monitoring and personalized medicine. However, there is still a long path toward complete market adoption and acceptance of this fascinating technology. Accordingly, microfluidic science and technology can provide excellent solutions for bridging the gap between basic research and clinical research. The research gap has led to the emerging field of epidermal microfluidics. Moreover, recent advances in the fabrication of highly flexible and stretchable microfluidic systems have revived the concept of micro elastofluidics, which can provide viable solutions for on-skin wearable biofluid handling. In this context, this review highlights the current state-of-the-art platforms in this field and discusses the potential technologies that can be used for on-skin wearable devices. Toward this aim, we first compare various microfluidic platforms that could be used for on-skin wearable devices. These platforms include semiconductor-based, polymer-based, liquid metal-based, paper-based, and textile-based microfluidics. Next, we discuss how these platforms can enhance the stretchability of on-skin wearable biosensors at the device level. Next, potential microfluidic solutions for collecting, transporting, and controlling the biofluids are discussed. The application of finger-powered micropumps as a viable solution for precise and on-demand biofluid pumping is highlighted. Finally, we present the future directions of this field by emphasizing the applications of droplet-based microfluidics, stretchable continuous-flow micro elastofluidics, stretchable superhydrophobic surfaces, liquid beads as a form of digital micro elastofluidics, and topological liquid diodes that received less attention but have enormous potential to be integrated into on-skin wearable devices.