Point-of-care (PoC) diagnostics is promising for early detection of a number of diseases, including cancer, diabetes, and cardiovascular diseases, in addition to serving for monitoring health conditions. To be efficient and cost-effective, portable PoC devices are made with microfluidic technologies, with which laboratory analysis can be made with small-volume samples. Recent years have witnessed considerable progress in this area with “epidermal electronics”, including miniaturized wearable diagnosis devices. These wearable devices allow for continuous real-time transmission of biological data to the Internet for further processing and transformation into clinical knowledge. Other approaches include bluetooth and WiFi technology for data transmission from portable (non-wearable) diagnosis devices to cellphones or computers, and then to the Internet for communication with centralized healthcare structures. There are, however, considerable challenges to be faced before PoC devices become routine in the clinical practice. For instance, the implementation of this technology requires integration of detection components with other fluid regulatory elements at the microscale, where fluid-flow properties become increasingly controlled by viscous forces rather than inertial forces. Another challenge is to develop new materials for environmentally friendly, cheap, and portable microfluidic devices. In this review paper, we first revisit the progress made in the last few years and discuss trends and strategies for the fabrication of microfluidic devices. Then, we discuss the challenges in lab-on-a-chip biosensing devices, including colorimetric sensors coupled to smartphones, plasmonic sensors, and electronic tongues. The latter ones use statistical and big data analysis for proper classification. The increasing use of big data and artificial intelligence methods is then commented upon in the context of wearable and handled biosensing platforms for the Internet of things and futuristic healthcare systems.