Microfluidics platforms can program small amounts of fluids to execute a bio-protocol, and thus, can automate the work of a technician and also integrate a large part of laboratory equipment. Although most microfluidic systems have considerably reduced the size of a laboratory, they are still benchtop units, of a size comparable to a desktop computer. In this paper, we argue that achieving true mobility in microfluidics would revolutionize the domain by making laboratory services accessible during traveling or even in daily situations, such as sport and outdoor activities. We review the existing efforts to achieve mobility in microfluidics, and we discuss the conditions mobile biochips need to satisfy. In particular, we show how we adapted an existing biochip for mobile use, and we present the results when using it during a train ride. Based on these results and our systematic discussion, we identify the challenges that need to be overcome at technical, usability and social levels. In analogy to the history of computing, we make some predictions on the future of mobile biochips. In our vision, mobile biochips will disrupt how people interact with a wide range of healthcare processes, including medical testing and synthesis of on-demand medicine.