As robotic technology advances, robots continue to work in ever closer proximity to humans. From vacuuming robots to wearable robots, today's autonomous systems must be able to reason about nearby humans that may seek to interact or collaborate. It is especially critical for robots that interact with humans physically to be able to ensure the safety and efficacy of the collaboration. Perhaps the closest physical human/robot interaction (HRI) is for rehabilitative exoskeletons used in the physical therapy clinic, such as those used to re-train walking for people who have had a spinal cord injury. To create fluid normative gait patterns, the exoskeleton must be able to estimate the user's intended movements and then assist them in achieving those movements. Several practical challenges prevent current exoskeleton devices from achieving this ideal of human/robot interaction. This dissertation seeks to provide fundamental advances in support of physical HRI by addressing how to model exoskeleton-assisted gait mechanics, and to characterize, estimate, and realize human gait intentions. Existing strategies of modeling unassisted human gait have been useful for informing the control of bipedal robots in the past, but it is unclear how well these models characterize the salient features of exoskeleton-assisted gait. Furthermore, it is not well documented how measured or derived signals respond when the exoskeleton user changes their gait intentions. A more thorough understanding of these intent-related signals can inform the process by which intentions are estimated in real time. Once the user's intentions are estimated, it remains an open challenge to determine how the robot should respond to these intentions in a safe and effective manner. The work in this dissertation first relates existing data-driven and physics-based models of unassisted human walking to steady-state exoskeleton-assisted gait before investigating the nature of intent-related signals when the user makes an intent change. A human subject experiment with a commercial exoskeleton shows that intent-related information can be inferred via sensors integrated with the rigid structure of the exoskeleton. The utility of these signals is demonstrated by the development of an algorithm that identifies intentions to speed up or slow down with a maximum accuracy of 87%. Finally, preliminary work shows that trajectory optimization is one method by which the exoskeleton can plan for safe optimal actions that incorporate information about the physical human/robot interaction. While this dissertation seeks to enable intent-informed control for the exoskeleton, the main contribution of this work is in expanding the fundamental understanding of physical HRI, including how to model HRI systems, how to analyze intent-related signals, and how to identify human intentions in real time.