Practical realization of model-based dynamic legged behaviors is substantially more challenging than statically stable behaviors due to their heavy dependence on second-order system dynamics. This problem is further aggravated by the dif- ficulty of accurately measuring or estimating dynamic parameters such as spring and damping constants for associated models and the fact that such parameters are prone to change in time due to heavy use and associated material fatigue. In the first part of this thesis, we present an on-line, model-based adaptive control method for running with a planar spring-mass hopper based on a once-per-step parameter correction scheme. Our method can be used both as a system identifi- cation tool to determine possibly time-varying spring and damping constants of a miscalibrated system, or as an adaptive controller that can eliminate steady-state tracking errors through appropriate adjustments on dynamic system parameters. We use Spring-Loaded Inverted Pendulum (SLIP) model, which is the mostly used, effective and accurate descriptive tool for running animals of different sizes and morphologies, to evaluate our algorithm. We present systematic simulation studies to show that our method can successfully accomplish both accurate tracking and system identification tasks on this model. Additionally, we extend our simulations to Torque-Actuated Dissipative Spring-Loaded Inverted Pendulum (TD-SLIP) model towards its implementation on an actual robot platform. In the second part of the thesis, we present the design and construction of a onelegged hopping robot we built to test the practical applicability of our adaptive control algorithm. We summarize the mechanical, electronics and software design of our robot as well as the performed system identification studies to calibrate the unknown system parameters. Finally, we investigate the robot’s motion achieved by a simple torque-actuated open loop controller.