Music Therapy is a therapeutic practice that may include one or more of several activities involving music. No music experience is necessary but therapy may include learning how to play an instrument or to create music. It might simply be listening to music.
Music Therapy is defined by the Certification Board for Music Therapists as “…the specialized use of music by a credentialed professional who develops individualized treatment and supportive interventions for people of all ages and ability levels to address their social, communication, emotional, physical, cognitive, sensory, and spiritual needs.” While listening might be therapeutic, the therapeutic application would be different from donning a pair of headphones and listening to your favorite tunes.
There are specialized areas of MT, like Neurologic MT that treats the brain and Creative Arts Therapy, which focuses on self-expression.
A number of studies have been done and the outcomes are largely positive. You can find scholarly articles for studies on music therapy for children and adolescents with psychopathology, for dementia patients, for premature infants, hospital patients, people with depression, stroke patients, children with autism, and many more. Efficacy varies but MT appears overall to be useful for treating anxiety and depression and increasing attention span and quality of life.