This work reviews the growing body of interdisciplinary research on music cognition, using biomechanical, kinesiological, clinical, psychosocial, and sociological methods. The review primarily examines the relationship between temporal elements in music and motor responses under varying contexts, with considerable relevance for clinical rehabilitation. After providing an overview of the terminology and approaches pertinent to theories of rhythm and meter from the musical-theoretical and cognitive fields, this review focuses on studies on the effects of rhythmic sensory stimulation on gait, rhythmic cues' effect on the motor system, reactions to rhythmic stimuli attempting to synchronize mobility (i.e., musical embodiment), and the application of rhythm for motor rehabilitation for individuals with Parkinson's disease, stroke, mild cognitive impairment, Alzheimer's disease, and other neurodegenerative or neurotraumatic diseases. This work ultimately bridges the gap between the musical-theoretical and cognitive science fields to facilitate innovative research in which each discipline informs the other.