Emerging wearable and implantable biodevices have been significantly revolutionizing the diagnosis and treatment of disease. However, the geometrical mismatch between tissues and biodevices remains a great challenge for achieving optimal performances and functionalities for biodevices. Shape-adaptable biodevices enabling active compliance with human body tissues offer promising opportunities for addressing the challenge through programming their geometries on demand. This article reviews the design principles and control strategies for shape-adaptable biodevices with programmable shapes and actively compliant capabilities, which have offered innovative diagnostic/therapeutic tools and facilitated a variety of wearable and implantable applications. The state-of-the-art progress in applications of shape-adaptable biodevices in the fields of smart textiles, wound care, healthcare monitoring, drug and cell delivery, tissue repair and regeneration, nerve stimulation and recording, and biopsy and surgery, is highlighted. Despite the remarkable advances already made, shape-adaptable biodevices still confront many challenges on the road toward the clinic, such as enhanced intelligence for actively sensing and operating in response to physiological environments. Next-generation paradigms will shed light on future directions for extending the breadth and performance of shape-adaptable biodevices for wearable and implantable applications.