We aim at designing, prototyping, and validating a new generation of ICT hardware and software technologies inspired from plant roots, called PLANTOIDS, endowed with distributed sensing, actuation, and intelligence for tasks of environmental exploration and monitoring. PLANTOIDS take inspiration from, and aim at reproducing, the amazing penetration, exploration, and adaptation capabilities of plant roots. Plants have evolved very robust growth behaviours to respond to changes in their environment and a network of highly sensorized branching roots to efficiently explore the soil volume, mining minerals and up-taking water. PLANTOID has two major goals: 1) to abstract and synthesize with robotic artefacts the principles that enable plant roots to effectively and efficiently explore and adapt to underground environments; 2) to formulate scientifically testable hypotheses and models of some unknown aspects of plant roots, such as the role of local communication among root apices during adaptive growth and the combination of rich sensory information to produce collective decisions. The PLANTOID artefact will be composed of a network of sensorized and actuated roots, displaying rich sensing and coordination capabilities as well as energy-efficient actuation and high sustainability, typical of the Plant Kingdom. Each PLANTOID root will consist of an apex that comprises sensors, actuators, control units, and by an elongation zone that mechanically connects the apex and the trunk of the robot. The new technologies expected to result from PLANTOID concern energy-efficient actuation systems, chemical and physical micro-sensors, sensor fusion techniques, kinematics models, and distributed, adaptive control in networked structures with local information and communication capabilities. The foundational research program of PLANTOID will be carried out by a consortium of engineers, plant biologists, and computer scientists with demonstrated experience in interdisciplinary work.