In the era of Internet-of-things, many things can stay connected; however, biological systems, including those necessary for human health, remain unable to stay connected to the global Internet due to the lack of soft conformal biosensors. The fundamental challenge lies in the fact that electronics and biology are distinct and incompatible, as they are based on different materials via different functioning principles. In particular, the human body is soft and curvilinear, yet electronics are typically rigid and planar. Recent advances in materials and materials design have generated tremendous opportunities to design soft wearable bioelectronics, which may bridge the gap, enabling the ultimate dream of connected healthcare for anyone, anytime, and anywhere. We begin with a review of the historical development of healthcare, indicating the significant trend of connected healthcare. This is followed by the focal point of discussion about new materials and materials design, particularly low-dimensional nanomaterials. We summarize material types and their attributes for designing soft bioelectronic sensors; we also cover their synthesis and fabrication methods, including top-down, bottom-up, and their combined approaches. Next, we discuss the wearable energy challenges and progress made to date. In addition to front-end wearable devices, we also describe back-end machine learning algorithms, artificial intelligence, telecommunication, and software. Afterward, we describe the integration of soft wearable bioelectronic systems which have been applied in various testbeds in real-world settings, including laboratories that are preclinical and clinical environments. Finally, we narrate the remaining challenges and opportunities in conjunction with our perspectives.