A symbiotic robotic system consists of a robot, a human, and a (smart) environment that cooperate symbiotically to perform a task. While the possibility of cooperating with the smart environment and with humans might greatly simplify the execution of robotic tasks, it also presents new challenges that open new research directions. In this article, we claim that symbiotic robotic systems will constitute a dominant new paradigm in the future of autonomous robotics, and discuss the corresponding potential and scientific challenges. This article is part of a special issue on the Future of AI.