The future of computing can be embodied autonomy - robots seamlessly interacting with humans, agents making trustworthy decisions, and pervasive intelligence advancing toward AGI. However, the growing complexity of embodied agents imposes significant computing challenges, including increased latency, memory demands, energy consumption, safety concerns, and higher design costs, all of which hinder the widespread deployment of agentic and embodied intelligence. This dissertation presents a full-stack software-system-hardware co-optimization framework for embodied intelligence. By integrating application discovery, systems thinking, co-design intelligence, and chip tapeout demonstration, the research establishes systematic methodologies for domain-specific optimization. Through case studies in compositional neuro-symbolic reasoning, cooperative long-horizon planning, and autonomous navigation, it demonstrates how our tailored computing methodology identifies critical domain characteristics, generates optimized architectures and system designs, and achieves improvements in performance, adaptability, efficiency, and reliability, all while sustainably shaping our digital future and unlocking the potential of physical and embodied intelligence.