A large body of compelling evidence has been accumulated demonstrating that embodiment - the agent's physical setup, including its shape, materials, sensors and actuators - is constitutive for any form of cognition and as a consequence, models of cognition need to be embodied. In contrast to methods from empirical sciences to study cognition, robots can be freely manipulated and virtually all key variables of their embodiment and control programs can be systematically varied. As such, they provide an extremely powerful tool of investigation. We present a robotic bottom-up or developmental approach, focusing on three stages: (a) low-level behaviors like walking and reflexes, (b) learning regularities in sensorimotor spaces, and (c) human-like cognition. We also show that robotic based research is not only a productive path to deepening our understanding of cognition, but that robots can strongly benefit from human-like cognition in order to become more autonomous, robust, resilient, and safe.