Soft (flexible and stretchable) biosensors have great potential in real-time and continuous health monitoring of various physiological factors, mainly due to their better conformability to soft human tissues and organs, which maximizes data fidelity and minimizes biological interference. Most of the early soft sensors focused on sensing physical signals. Recently, it is becoming a trend that novel soft sensors are developed to sense and monitor biochemical signals in situ in real biological environments, thus providing much more meaningful data for studying fundamental biology and diagnosing diverse health conditions. This is essential to decentralize the healthcare resources towards predictive medicine and better disease management. To meet the requirements of mechanical softness and complex biosensing, unconventional materials, and manufacturing process are demanded in developing biosensors. In this review, we summarize the fundamental approaches and the latest and representative design and fabrication to engineer soft electronics (flexible and stretchable) for wearable and implantable biochemical sensing. We will review the rational design and ingenious integration of stretchable materials, structures, and signal transducers in different application scenarios to fabricate high-performance soft biosensors. Focus is also given to how these novel biosensors can be integrated into diverse important physiological environments and scenarios in situ, such as sweat analysis, wound monitoring, and neurochemical sensing. We also rethink and discuss the current limitations, challenges, and prospects of soft biosensors. This review holds significant importance for researchers and engineers, as it assists in comprehending the overarching trends and pivotal issues within the realm of designing and manufacturing soft electronics for biochemical sensing.