Current robotic control methods take advantage of high computing power to compute trajectories and perform optimal movements for a given task, yet these robots still fall far short of their animal counterparts when interacting with the environment. Animals dynamically adapt to varying terrain and small perturbations almost effortlessly. In order to improve our robotic systems and build better control methods, it makes sense to look more closely at how animals solve this interaction. In this work, I developed a control model of mammalian walking with models grounded in neuroscience and computational neuroscience. First, I developed a neuromechanical model of a rat with 14 degrees of freedom and 28 muscles, and I explored how hypothesized neural architectures can be used to coordinate four limbs in a walking gait for a rat. Additionally, through simulated ablation experiments, I developed hypotheses on how inter-leg pathways work together to maintain limb timing. After this, I developed a procedure to train the neural system to produce dynamic walking in both a rat simulation and a robot named Puppy. This method works by first using a model of the system (rat or robot) to determine required motor neuron activations to produce stable walking. For the robot, this required building a force-length-pressure model of the McKibben actuators to enable accurate force control. Parameters in the neural system are then set such that it produces similar activations to the desired pattern. I applied the same training procedure to both the simulated rat and the robot and show that it is capable of producing continuous, self-supported stepping in both systems.