I'll try to answer this question by describing the boundaries of psych and neurosurgery with relation to neurology. There is a lot of overlap. Psychiatry deals with behavioral disorders, which of course are generated in the brain and can be treated with drugs that manipulate neurotransmitters. However, psychiatrists defer to neurologists when there may be "organic" disease causing a patient's behavioral symptoms.Organic means a systemic disease or a disease process that is not just causing behavioral symptoms. So maybe a psychiatrist or a neurologist could care for a patient who is psychotic, but when they do a CT of the head and see something abnormal, they call the neurologists. There is a subspecialty of neurology called behavioral neurology which deals with odd disorders of perception after stroke or Alzheimers disease. There is also a weird reverse of this relationship, where patients will present with bona-fide neurological symptoms like a seizure, weakness, or visual loss, but nothing is found and it is determined that the symptoms are psychosomatic or something called "conversion disorder", and in that case the neurologists call the psychiatrists for help!
Neurosurgeons are surgeons, and they like to get their hands dirty. Anything anatomically wrong in the brain or spinal cord is possible. So diseases like acute or subacute brain bleeds, brain or spinal cord trauma, brain tumors, brain abcesses or cysts, certain vascular conditions in the brain like aneurysms, etc are the domain of the neurosurgeons. But again there is lots of overlap and neurosurgeons are neurologists are often BFFs.
There are other things for neurologists to do, too. There are neuromuscular diseases like mysasthenia gravis and all the muscular dystrophies. Pain/headache specialists. Movement disorder specialists. Neuro-interventional. Neuro-critical care.
