This paper explores current developments in evolutionary and bio-inspired approaches to autonomous robotics, concentrating on research from our group at the University of Sussex. These developments are discussed in the context of advances in the wider fields of adaptive and evolutionary approaches to AI and robotics, focusing on the exploitation of embodied dynamics to create behaviour. Four case studies highlight various aspects of such exploitation. The first exploits the dynamical properties of a physical electronic substrate, demonstrating for the first time how component-level analog electronic circuits can be evolved directly in hardware to act as robot controllers. The second develops novel, effective and highly parsimonious navigation methods inspired by the way insects exploit the embodied dynamics of innate behaviours. Combining biological experiments with robotic modeling, it is shown how rapid route learning can be achieved with the aid of navigation-specific visual information that is provided and exploited by the innate behaviours. The third study focuses on the exploitation of neuromechanical chaos in the generation of robust motor behaviours. It is demonstrated how chaotic dynamics can be exploited to power a goal-driven search for desired motor behaviours in embodied systems using a particular control architecture based around neural oscillators. The dynamics are shown to be chaotic at all levels in the system, from the neural to the embodied mechanical. The final study explores the exploitation of the dynamics of brain-body-environment interactions for efficient, agile flapping winged flight. It is shown how a multi-objective evolutionary algorithm can be used to evolved dynamical neural controllers for a simulated flapping wing robot with feathered wings. Results demonstrate robust, stable, agile flight is achieved in the face of random wind gusts by exploiting complex asymmetric dynamics partly enabled by continually changing wing and tail morphologies.