Sensorimotor synchronization (SMS), the coordination of physical actions in time with a rhythmic sequence, is a skill that is necessary not only for keeping the beat when making music, but in a wide variety of interpersonal contexts. Being able to attend to temporal regularities in the environment is a prerequisite for event prediction, which lies at the heart of many cognitive and social operations. It is therefore of value to assess and potentially stimulate SMS abilities, particularly in aging and neurocognitive disorders (NCDs), to understand intra-individual communication in the later stages of life, and to devise effective music-based interventions. While a bulk of research exists about SMS and movement-based interventions in Parkinson’s disease, a lot less is known about other types of neurodegenerative disorders, such as Alzheimer’s disease, vascular dementia, or frontotemporal dementia. In this review, we outline the brain and cognitive mechanisms involved in SMS with auditory stimuli, and how they might be subject to change in healthy and pathological aging. Globally, SMS with isochronous sounds is a relatively well-preserved skill in old adulthood and in patients with NCDs. At the same time, natural tapping speed decreases with age. Furthermore, especially when synchronizing to sequences at slow tempi, regularity and precision might be lower in older adults, and even more so in people with NCDs, presumably due to the fact that this process relies on attention and working memory resources that depend on the prefrontal cortex and parietal areas. Finally, we point out that the effect of the severity and etiology of NCDs on sensorimotor abilities is still unclear: More research is needed with moderate and severe NCD, comparing different etiologies, and using complex auditory signals, such as music.