The three major parts of the brain stem are the

-The medulla which controls breathing swallowing blood pressure and heart rate.

-The pons which links the cerebellum to the cerebrum.

-The midbrain which governs rudimentary vision and hearing.

If you are referring to the human brain, then the answer is that the brain stem consists of the midbrain, the pons, and the medulla oblongata. The brain stem connects the brain with the spine and these three parts are essential to it, even though there may sometime be a part called the diencephalon. Animals have different brain compositions than humans.