This project examines the dynamics and design of control systems for a rocket in propulsive ascent and descent using a simplified model with motion constrained to a vertical plane. The governing differential equations are analyzed. They are then linearized, after which transfer functions are derived relating controllable input variables to controlled output variables. The effect of changes in various parameters as well as other aspects of the system are examined. Methods for controller design based on the derived transfer functions are discussed. This will include the discussion of control of the final descent and landing of the rocket. Lastly, there is a brief discussion about both the successes and limitations of the model analyzed.