Flexible and stretchable bioelectronics provides a biocompatible interface between electronics and biological systems and has received tremendous attention for in situ monitoring of various biological systems. Considerable progress in organic electronics has made organic semiconductors, as well as other organic electronic materials, ideal candidates for developing wearable, implantable, and biocompatible electronic circuits due to their potential mechanical compliance and biocompatibility. Organic electrochemical transistors (OECTs), as an emerging class of organic electronic building blocks, exhibit significant advantages in biological sensing due to the ionic nature at the basis of the switching behavior, low driving voltage (<1 V), and high transconductance (in millisiemens range). During the past few years, significant progress in constructing flexible/stretchable OECTs (FSOECTs) for both biochemical and bioelectrical sensors has been reported. In this regard, to summarize major research accomplishments in this emerging field, this review first discusses structure and critical features of FSOECTs, including working principles, materials, and architectural engineering. Next, a wide spectrum of relevant physiological sensing applications, where FSOECTs are the key components, are summarized. Last, major challenges and opportunities for further advancing FSOECT physiological sensors are discussed.