Our research aims at the creation of fast and efficient running motions of four legged robotic systems. We design our robots to explicitly enable and exploit natural dynamic effects (such as the oscillation on springy legs) in their mechanical structure and their actuation with the goal of eliminating undesired negative work, minimizing the required actuator power, and alleviating shocks. For the variety of sub-problems that arise in this context (reaching from the proper hardware design to the efficient excitation and stabilization of the desired motion), we will present two complementary approaches: Firstly, by employing the concept of operational space control, we are able to project the dynamics of simple conceptual models onto an actual robotic system. This is shown for an extended SLIP-model, but the same technique can be employed to other models for which we developed efficient gaits and control strategies. By considering the obtained torques as a function of joint positions, we can then specifically design elastic elements that passively support the actuators. Secondly, we implemented a limit cycle based, optimal control approach using a Fourier series to efficiently excite the dynamics of a given robot or model – a method that was employed to identify different bounding gaits for a conceptual quadruped model, and to drive the most recent prototype of our robotic leg.