The swimming of a simple vertebrate, the lamprey, can shed light on the coupling of neural signals to muscle mechanics and passive body dynamics in animal locomotion. We will present recent progress in the development of a computational model of a lamprey with sensory feedback and examine the emergent swimming behavior of the coupled fluid-neural-muscle-body system. A long-term goal of this research is to investigate the relation of spinal chord injuries to movement in a very simple system. In addition, even though the fish's material properties most likely have a strong effect on swimming performance, it is extremely difficult to use animal experiments to identify its role. While one species of fish may be stiffer than another, they also typically differ in numerous other ways, such as the anatomy of the muscle and skeleton and the way they activate their muscles during swimming. We will discuss how computational and robotic models offer a more controlled way to probe the effects of body stiffness.