The goal of the research presented in this thesis is to increase the understanding of the human running gait. The understanding of the human running gait is essential for the development of devices, such as prostheses and orthoses, that enable disabled people to run or that enable able people to increase their running performance. Although these devices are currently being developed, there is not much insight yet in the fundamentals of the running gait. This fundamental knowledge is required for improving these devices. One of the big unknowns is how these devices affect the ability of the user to handle disturbances, like sudden pushes or variations in floor height. To gain insight in the fundamentals of the human running gait and the disturbance rejection behavior in particular, the gait synthesis approach is taken. In this approach, the running gait is studied by synthesizing the human running on simulation models and on robots. This allows studying the effects of specific system parameters in a simplified and controlled environment. A number of simulation models and a physical running robot have been developed. The simulation models vary in complexity, from simple simulation models based on the well-known spring loaded inverted pendulum (SLIP) model to simulation models that closely resemble the physical running robot. The simple simulation models are useful to get fundamental insights, due to their simple dynamics. The results of the simple models are validated with the more realistic models and physical running robot. This thesis focuses on the effect of three important system parameters on the disturbance rejection behavior. These three parameters are: the leg stiffness profile, the location of the center-of-mass, and the swing-leg retraction rate. These three parameters were selected, based on our experience with walking robots. The research in this thesis shows that the effects of these parameters are the following. The leg stiffness profile has a significant influence on the disturbance rejection behavior. For a simple running model, we show that nonlinear leg springs can improve the disturbance rejection up to a factor 7 compared to the optimal linear leg spring. The optimal leg stiffness profile for the maximal disturbance rejection behavior is strongly nonlinear. These results show that the generally used linear leg springs are far from optimal in terms of disturbance rejection behavior. The location of the center-of-mass of the torso also has a large influence on the disturbance rejection. The optimal center-of-mass location depends on the type of the expected disturbance, which is above the hip for floor height disturbances and below the hip for push disturbances on the center-of-mass. The commonly used center-of-mass location at the hip is far from optimal. An offset of the center-of-mass location can increase the disturbance rejection up to a factor 10 compared to the center-of-mass at the hip. The swing-leg retraction rate, the speed of the backwards rotation of the front leg prior to touchdown, affects the disturbance rejection rate. We show that this effect is maximal at a mild retraction rate, which is much lower than the retraction rate for ground speed matching. The optimal retraction rate decreases with increasing running velocity. Besides improving disturbance rejection, swing-leg retraction can also reduce energetic losses, impact forces, and the risk of slipping. However, we show that all of the benefits of swing-leg retraction occur at different retraction rates, which indicates that there is an inherent tradeoff to consider when selecting the retraction rate for a robot control system. In addition, the effect of the retraction rate on these benefits is strongly model and/or parameter dependent, making it difficult to make general rules on how to select the retraction rate. Besides the above-mentioned results, this research also revealed the following insights. Firstly, not all results from simple running model studies transfer well to more realistic models and robots. This is especially the case for studies on effects that involve impact dynamics, as impact dynamics greatly depend on the leg morphology. Secondly, the gait sensitivity norm, the disturbance rejection measured introduced by Hobbelen for walking systems, is also suitable for running systems. Finally, the implementation of a spring in parallel with the actuator in the knee joint can greatly reduce the required actuator torque and power. Overall, the results of this thesis show that there are many opportunities to improve the disturbance rejection performance of bipedal running robots. This can be done either by mechanical changes to the robotics system, e.g. implementing a nonlinear leg spring or placing the center-of-mass away from the hip, or by changes to the controller, e.g. implementing swing-leg retraction. The results of this thesis also point out promising directions for the development of better running orthoses and prostheses. Most promising is the implementation of nonlinear springs in exoskeletons, because the results show a large improvement in the disturbance rejection behavior and because nonlinear springs are relatively easy to implement in exoskeletons.