The majority of assistive exoskeletons are designed to rigidly track time-based kinematic patterns using highly geared actuators, which prevents users from moving their joints freely without help from the exoskeleton. Individuals with partial or full volitional control of their lower extremities require novel design and control methods for exoskeletons that are more compatible with human interaction. To assist or augment volitional human motion, exoskeleton joints must be backdrivable, and the control strategy must be invariant to the user's joint kinematics. This article presents the design philosophy behind two generations of highly backdrivable exoskeletons, which utilize torque-dense motors with low-ratio transmissions. To leverage these designs, a torque-based control framework is presented that shapes the human body's kinetic and potential energies to provide trajectory-free assistance. Simulations with a human-like biped demonstrate the effects of different energyshaping control strategies, and experiments with a powered knee-ankle exoskeleton show the user-cooperative and task-invariant nature of the control approach. These results exhibit potential value for gait assistance and augmentation without being constrained to a clinical environment like traditional treadmill training devices. To achieve the control design and implementation, knowledge of linear algebra, robot dynamics, state-space control, and LabVIEW programing is needed. © 2018 IEEE.