Even as they continue to improve, legged robots pale in comparison to their biological counterparts. This discrepancy is at least partly due to robots possessing an order of magnitude fewer degrees of freedom. In fact, most dynamically capable quadrupedal robots lack any degrees of freedom in the torso, opting instead for a simpler, single, rigid body. This rigidity results in the legs competing for workspace and power optimality during locomotion. Furthermore, although some quadrupeds do feature a flexible torso, most research primarily focuses on bending in either the sagittal or lateral planes. In contrast, this thesis explores the integration of the often-neglected axially twisting spinal degree of freedom into quadrupedal robotic platforms towards achieving more agile dynamic legged robots. First, this work introduces “Twist”, a novel quadrupedal robotic platform with an axially twisting spine and the challenges that are inherent to this new design. Second, taking inspiration from biomechanical reorientation data in geckos, the thesis develops an axial twisting strategy that reduces the effort required for a robot to right itself after falling. Following this, a trajectory-optimization-based study compares the energetic and dynamic performance of two quadrupedal models, one with a rigid torso and one with a twisting torso, across various dynamic and aperiodic locomotory tasks. Hoping to realize these results with Twist, the thesis proceeds to develop controllers for agile, spatial locomotion. Starting in the sagittal plane, an angular-momentum-based coordinate is developed for a three-degree-of-freedom, extensible inverted pendulum model and is shown to be an approximate asymptotic phase variable and to produce an input decoupling. Toward generalizing those results, the underactuation of the spatial floating torso model during two-point contact is thoroughly examined and informs a composition-based controller for the “Twist” platform. Finally, integrating these ideas, this thesis develops a trotting gait, which shows promising results using this composition for spatial quadrupedal locomotion. These compositions will act as stepping stone toward controlling transitional and dynamic behaviors on quadrupedal robots with flexible spines.