In nature, quadrupedal mammals can run at high speeds over uneven terrain, turn sharply, jump obstacles, and stop suddenly. While these abilities are common features in biological locomotion, they represent remarkable feats from both an engineering and control perspective. Although some robots over the past several decades have been capable of dynamic running gaits, none have adequately demonstrated the gallop, the preferred gait of high-speed quadrupedal locomotion for most quadrupeds; and none have been capable of high-speed dynamic maneuvering, especially the turn. There are several reasons for the lack of progress in high-speed locomotion and maneuvering. First, the concept of dynamic stability, where the system undergoes recurring periods of statically unstable motion, requires a different approach for control that must rely in part on the natural dynamics of the system, while affording only limited time for significant control actions. Furthermore, traditional analytical techniques used in control design typically require simplifying assumptions for both the dynamic model and the gait. To date, these approaches have failed to generate usable results for systems with more biologically motivated designs and for complex, asymmetric high-speed gaits like the gallop. Since high-speed gaits like the gallop remain out of reach, dynamic maneuvering has remained a distant goal, as well. Furthermore, dynamic maneuvers involve significant acceleration and, consequently, large peak power requirements, which appear to be largely beyond the capabilities of standard actuators. Finally, studying dynamic maneuvers is difficult because they typically occur at high speeds and over highly varying terrain, conditions which are difficult to reproduce in a laboratory environment and equally difficult to manage when studying maneuvers in biological systems. In this work, a practical approach is developed to study various high-speed locomotion behaviors such as galloping, turning, jumping, and stopping in a simulated quadrupedal model with biologically-based characteristics. A flexible control architecture comprised of low-level primitive functions for each leg is used to create the various behaviors by combining the functions sequentially. A multiobjective genetic algorithm (MOGA) is then used to search for parameter values for these functions, where the search space is minimized by efficient parameterization of each leg-level primitive function. Results for the 3D gallop, high-speed turn, running jump, jump-start, and sudden stop are presented, which represent new results for a simulated system of this complexity. Furthermore, the resulting behaviors mimic biological motion, providing important data on the underlying mechanics required to achieve this level of locomotion. Dynamic characterization of each behavior promises to facilitate the future development of real-time controllers for galloping and maneuvering in a quadruped robot. A final demonstration of galloping and maneuvering is presented to illustrate the effectiveness of the approach.