Advances in wireless technologies, low-power electronics, the internet of things, and in the domain of connected health are driving innovations in wearable medical devices at a tremendous pace. Wearable sensor systems composed of flexible and stretchable materials have the potential to better interface to the human skin, whereas silicon-based electronics are extremely efficient in sensor data processing and transmission. Therefore, flexible and stretchable sensors combined with low-power silicon-based electronics are a viable and efficient approach for medical monitoring. Flexible medical devices designed for monitoring human vital signs, such as body temperature, heart rate, respiration rate, blood pressure, pulse oxygenation, and blood glucose have applications in both fitness monitoring and medical diagnostics. As a review of the latest development in flexible and wearable human vitals sensors, the essential components required for vitals sensors are outlined and discussed here, including the reported sensor systems, sensing mechanisms, sensor fabrication, power, and data processing requirements.