The rapid growth of artificial intelligence (AI) is increasingly constrained by fundamental hardware bottlenecks in computation throughput and energy efficiency. Bioinspired computing (BIC) offers a promising alternative by emulating the intrinsic advantages of biological systems, such as parallelism, adaptability, and robustness. Progress in BIC hardware demands interdisciplinary convergence that bridges materials science and device physics with neuroscience, computer science, mathematics, and information science. Therefore, the development of this cross-disciplinary field urgently requires a comprehensive roadmap that analyzes systematically and in-depth the frontier issues and the latest progress. In this roadmap, we categorize the critical challenges into three components: hardware foundations, architectures, and prototype realizations. We highlight how biological features inspire the design of BIC hardware through device physics and discuss their performance metrics and engineering challenges. We then describe how diverse signaling rules and structural organizations in BIC architectures support specific computational prototypes, including electronic and photonic BIC chips, and present a technological roadmap that outlines opportunities to expand the functional scope of BIC hardware through coordinated advances in devices, architectures, and system demonstrations. This ongoing convergence of interdisciplinary knowledge can help accelerate the shift toward high-efficiency AI hardware.