According to Joseph Chilton Pearce, there are five "brains," each building upon the other. Pearce writes: "at each stage of development each new system is dependent upon the full function of the system that developmentally preceded it."  Both Pearce and Ken Wilber say that a smaller and smaller portion of the human population makes it to each higher level of brain development.
At the bottom of the pyramid is the old reptilian brain. This is probably what Freud would have called the Id. It's the survival instinct and the reproductive urge on a sensory-motor level.
Above that is the old mammalian brain, the limbic system, which controls basic emotions of fear, pleasure, and anger. It feeds our basic emotional needs of hunger, sex, power, control, and nurturing. What Freud calls the Ego begins here. This feeling and remembering brain holds the pain body that goes deep and can even "possess" us for decades after we've been hurt. This brain is necessary because it gives us the emotional intelligence by which we read the meanings and social cues of daily interactions. It can be either a helpful emotional program or a wounded and angry one. It largely resides in our unconscious, only brought to the surface by either conflict or honest insight.
Next is the new mammalian brain or the neo-cortex. This too contributes to our egoic self. The neo-cortex has two hemispheres--the left brain and the right brain. The left or logical brain focuses on analytical, sequential, and logical thinking. The left brain deals with old, familiar, settled material that you have made logical and orderly. If you are primarily left-brained, you can become very logical but also very rigid and, as you get older, respond from the few neural grooves you've used in repetitive ways. You may not be able to understand people who don't think exactly like you do. Without collaboration with the right brain, there is not much capacity for empathy or solidarity, much less intimacy with others.
The right or creative brain is nonverbal and intuitive, using images rather than words to find and express meaning. It is the part of the brain that can deal with new material in new ways. Both hemispheres are important and both need education and development by mentoring and modeling. The right brain, however, has far more connections to the next level of the brain, the prefrontal lobes. That's why right-brained people can often be more imaginative and can adjust better to change. This may also be an aspect of spiritual intelligence.
The left brain apparently does not have many neural connections to the two remaining "higher" brains. So you normally need some encounter with mystery, paradox, non-rational truth or beauty, and inconsistency itself in order to develop your right/creative brain, and therefore the next two brains. This is why we grow through conflict and not through any easy order or the maintaining of comfort. I believe this is what Jesus means when he shockingly says, "I have come not to bring peace, but the sword" (Matthew 10:34). Most of Jesus' core teaching should put you in conflict with business as usual and with what you took for granted! The Gospel creates necessary conflicts that grow people up. What a shame that we made it into a simplistic answer book rather than read its deep transformative message.
Around age 15, a great brain surge begins in the prefrontal lobes. This is what I think Freud would have called the Superego. Historically, this was the age for initiation to assure the small ego would be given a great challenge at this time. Helicopter parents are of no help here. This developmental process integrates all the lower brains and aims you outward and upward. Myelination stabilizes all the neurons that have been used up to now. But all the synapses that have not been used are actually pruned away. What a loss to nature and the world! If there's no one loving our young people, believing in them, challenging them, and modeling for them the next stage, they fail to develop the potential of the prefrontal lobes, which connects them to the fifth brain. They inevitably become angry, sullen, and cynical.
The fifth brain is located in the heart--literally, the muscular organ that circulates our life-blood. All of the poetry and songs about the heart "knowing" were not just idle chatter; we now have scientific validation that the heart shares brain-like functions. The connection of the prefrontal lobes to the heart has been demonstrated electromagnetically and at the neural and hormonal levels too. 
The simplest indicator that someone is living at all of the brain's levels is that they are not violent in thought, word, or action. They do not need to hurt or humiliate the other or themselves. It doesn't mean that they cannot say hard things, but it doesn't come from a place of malice or a desire to cause pain. Quite frankly, they can "understand" the human soul. They are humans themselves!