Understanding brain function is one of the most important open problems in science today. At present, there is no concrete theory for how the brain works. Here, a theory is presented that provides a detailed mechanistic biological account of the brain’s capacities. Brain function is managed by a response (R) process that is structurally similar to the immune response, and shows anatomical and molecular specificity. Different R process stages utilize different cortical layers, hippocampus fields, basal ganglia paths, GABAergic interneurons, cerebellum paths, and molecular agents such as dopamine, serotonin and opioids. We show how the R process supports hierarchical action sequences, language and thought. The theory is supported by a large body of experimental evidence in many modalities, and accounts for virtually all of the major facts known about the brain at the system level.