Plants are connected by an underground fungi network that provides them with nutrients, helps share resources, and extends their perception abilities. This mycorrhizal network, known as the Wood Wide Web, is crucial in maintaining healthy natural ecosystems and limiting global warming. Thus, it must be preserved to mitigate the speeding up of the carbon cycle and its effects on climate change. Robotics and Artificial Intelligence can offer concrete solutions for a deeper analysis of natural processes at the basis of this global change and for developing sustainable technologies. Based on that, I-Wood proposes a new virtual and physical robotic network paradigm inspired by the belowground fungus-mediated inter-plant communication and the associated collective behaviours. Specifically, I-Wood will study, extract and formalize the rules of plant-fungus interaction mechanisms to develop a plant-inspired decision-making model and a new generation of root-like robots to explore the soil with plant-inspired behaviours. By imitating plants, these distributed intelligent systems will co-develop morphology and behaviour in a dynamic environment. The impact and feasibility of the proposed approach will be tested in a mixed social network, scale-down in a confined environment, where robots will interact with natural plants to facilitate the development of mycorrhizal networks. Grounded on a solid multi-disciplinary approach, I-Wood will pave the way for new paradigms in robotics and embodied AI based on solutions that overcome the current animal-based or brain-based model, novel approaches for the use of robotics in biology, and for new scientific knowledge on plant community with a major significance for biodiversity and climate protection.