Mostly the old saying is true, and you don't regrow brain cells. Research is starting to show that in special areas of the brain, you do. New neurons come from mitosis in the subventricular zone and in the dentate gyrus (DG). Not a great deal is known about their function, but evidence suggests the news DG neurons migrate to the nearby hippocampus where some memories are formed, and loss of those new cells impairs memory. Very few new neurons are ever made, relative to the total you have, so you still can't regrow new neurons in most brain damaged areas. You do make new glial cells at injury sites, and they wall off damage, control blood flow, and fight infection in your brain.