Neuromorphic and brain-based robotics have enormous potential for furthering our understanding of the brain. By embodying models of the brain on robotic platforms, researchers can investigate the roots of biological intelligence and work towards the development of truly intelligent machines. This paper discusses the history of the field and its potential. We give examples of biologically inspired robot designs and neural architectures that lead to brain-based robots. Looking to the future, we consider the development of cognitive, or even conscious, robots that display the adaptability and intelligence of biological organisms.