Embodied Intelligence (EI) provides a foundational framework for understanding intelligent and adaptive behaviors in both biological and artificial systems. Emerging from early philosophical and scientific discussions on mind-body dualism, EI emphasises the intricate relationship between physical bodies and information processing, which enables meaningful sensory-motor interactions with the environment. Its theories and technologies span multiple disciplines, including mechanical, electrical and control engineering, as well as computer science and material sciences, making it a complex field for robotics researchers to navigate. However, a comprehensive understanding of EI is essential to addressing key challenges and avoiding the redundancy of past discoveries. This article introduces fundamental design principles of intelligent adaptive systems, followed by key paradigms in autonomous agent architectures, such as feedback control, behavior-based approaches, mechanical and material intelligence and embodied social interaction. It explores insights from biology, physics, cognitive science and philosophy, focusing on emerging applications in adaptive systems, human-robot collaboration and bio-hybrid technologies.