Although a number of papers have already discussed the relevance of brain research for education, the fundamental concepts and discoveries connecting education and the brain have not been systematically reviewed yet. In this paper, four of these concepts are presented and evidence concerning each one is reviewed. First, the concept of neuroplasticity is proposed as a "sine qua non" for linking education and the brain. Then, the concepts of neuronal recycling and inhibition are presented as two fundamental mechanisms of school learning that emphasize the importance of knowing the initial brain structure of learners and, finally, the concept of attention is discussed as a central concept for linking teaching and the brain.