Effective human locomotion requires adaptation of our movements in order to compensate for changes both in our own body and in the environment with which we interact. Locomotor adaptation processes can be investigated in the laboratory with a split-belt treadmill, which has two belts that are driven at different speeds to create novel environmental conditions. The motor system exerts its control of movement through muscle activity, either in a corrective (feedback) or a predictive manner, and relies on sensation to gather information about the environment and the consequences of movements. In the context of split-belt locomotor adaptation, adjustment of predictive mechanisms is assumed to be fundamental to the adaptation, but the role of corrective responses remains unknown. More generally, we lack quantitative descriptions of the temporal dynamics of muscle activity through locomotor adaptation. In this work, we first investigate the structure of rapid changes in muscle activity following transitions in walking conditions. We show that these corrective responses are indicative of sensorimotor adaptation in locomotion and that the analysis of said responses can be used to identify an age-related decline in sensorimotor recalibration. We build on these results to characterize muscle activity dynamics through linear time-invariant space-state models. This allows us to study the evolution of muscle activity at different timescales through a locomotor adaptation and deadaptation protocol, and the effect of no movement intervals in the decay of acquired motor memories. Finally, we address the problem of measuring sensory information available to subjects about the split-belt environment. Even though sensation is critical to both generate rapid feedback corrections and update predictions for future movements, we have limited knowledge about subjects ability to sense such changes in this environment. We contribute with a new quantification of just noticeable differences between the two belts speeds for healthy subjects, showing that previous assessments substantially underestimated sensitivity in this context. Taken together, our results provide a mathematical framework to gain insights into computations underlying locomotor adaptation evoked by split-belt walking. This is a necessary step toward the development of models to predict and manipulate human behavior in this context.