The increased demand for physiologically relevant in vitro human skin models for testing pharmaceutical drugs has led to significant advancements in skin engineering. One of the most promising approaches is the use of in vitro microfluidic systems to generate advanced skin models, commonly known as skin-on-a-chip (SoC) devices. These devices allow the simulation of key mechanical, functional and structural features of the human skin, better mimicking the native microenvironment. Importantly, contrary to conventional cell culture techniques, SoC devices can perfuse the skin tissue, either by the inclusion of perfusable lumens or by the use of microfluidic channels acting as engineered vasculature. Moreover, integrating sensors on the SoC device allows real-time, non-destructive monitoring of skin function and the effect of topically and systemically applied drugs. In this Review, the major challenges and key prerequisites for the creation of physiologically relevant SoC devices for drug testing are considered. Technical (e.g., SoC fabrication and sensor integration) and biological (e.g., cell sourcing and scaffold materials) aspects are discussed. Recent advancements in SoC devices are here presented, and their main achievements and drawbacks are compared and discussed. Finally, this review highlights the current challenges that need to be overcome for the clinical translation of SoC devices.