Biological living materials, such as animal bones and plant stems, are able to self-heal, regenerate, adapt and make decisions under environmental pressures. Despite recent successful efforts to imbue synthetic materials with some of these remarkable functionalities, many emerging properties of complex adaptive systems found in biology remain unexplored in engineered living materials. Here, we describe a three-dimensional printing approach that harnesses the emerging properties of fungal mycelia to create living complex materials that self-repair, regenerate and adapt to the environment while fulfilling an engineering function. Hydrogels loaded with the fungus Ganoderma lucidum are three-dimensionally printed into lattice architectures to enable mycelial growth in a balanced exploration and exploitation pattern that simultaneously promotes colonization of the gel and bridging of air gaps. To illustrate the potential of such mycelium-based living complex materials, we three-dimensionally print a robotic skin that is mechanically robust, self-cleaning and able to autonomously regenerate after damage.