Flexible devices and functional systems with elaborated three-dimensional (3D) architectures can endow better mechanical/electrical performances, more design freedom, and unique functionalities, when compared to their two-dimensional (2D) counterparts. Such 3D flexible devices/systems are rapidly evolving in three primary directions, including the miniaturization, the increasingly merged physical/artificial intelligence and the enhanced adaptability and capabilities of heterogeneous integration. Intractable challenges exist in this emerging research area, such as relatively poor controllability in the locomotion of soft robotic systems, mismatch of bioelectronic interfaces, and signal coupling in multi-parameter sensing. By virtue of long-time-optimized materials, structures and processes, natural organisms provide rich sources of inspiration to address these challenges, enabling the design and manufacture of many bioinspired 3D flexible devices/systems. In this Review, we focus on bioinspired 3D flexible devices and functional systems, and summarize their representative design concepts, manufacturing methods, principles of structure-function relationship and broad-ranging applications. Discussions on existing challenges, potential solutions and future opportunities are also provided to usher in further research efforts toward realizing bioinspired 3D flexible devices/systems with precisely programmed shapes, enhanced mechanical/electrical performances, and high-level physical/artificial intelligence.