Music has cognitive, psychosocial, behavioral and motor benefits for people with neurological disorders such as dementia, stroke, Parkinson's disease (PD) and Autism Spectrum Disorder (ASD). Here we discuss seven properties or ‘capacities’ of music that interact with brain function and contribute to its therapeutic value. Specifically, in its various forms, music can be engaging, emotional, physical, personal, social and persuasive, and it promotes synchronization of movement. We propose the Therapeutic Music Capacities Model (TMCM), which links individual properties of music to therapeutic mechanisms, leading to cognitive, psychosocial, behavioral and motor benefits. We review evidence that these capacities have reliable benefits for people with dementia, stroke, PD and ASD when employed separately or in combination. The model accounts for the profound value that music affords human health and well-being and provides a framework for the development of non-pharmaceutical treatments for neurological disorders.