Plants are connected to each other by an underground network of fungi that provide them with nutrients, help share resources, and extend their perception abilities. This mycorrhizal network, known as the Wood Wide Web, plays a crucial role in maintaining healthy natural ecosystems, and in limiting the global warming. Thus, it must be preserved in order to mitigate the speeding up of the carbon cycle and its effects on climate change. Robotics and Artificial Intelligence (AI) 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 paradigm of virtual and physical robotic networks inspired by the belowground fungus-mediated inter-plant communication and by the associated collective behaviours. Specifically, I-Wood will study, extract and formalize the rules of plant-fungus interaction mechanisms to develop: a plant-inspired perceptron-like model; and a new generation of plant-inspired robots able to explore soil using their roots with growing, ageing, branching, and elongating abilities in response to their network-augmented perception and implementing plant-inspired collective behaviours. By imitating plants, these distributed intelligent systems will co-develop morphology and behaviour in a dynamic environment. 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 real plants to facilitate the development of mycorrhizal networks. Grounded on a strong 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 plants community with a major significance for biodiversity and climate protection.