Neurologist Education and Training. A neurologist is a medical doctor or osteopath who has trained in the diagnosis and treatment of nervous system disorders, including diseases of the brain, spinal cord, nerves and muscles.eurologists perform neurological examinations of the nerves of the head and neck; muscle strength and movement; balance, ambulation, and reflexes; and sensation, memory, speech, language, and other cognitive abilities. They also perform diagnostic tests such as the following: 1  CAT (computed axial tomography) or CT scan.