Neuromodulators such as dopamine, serotonin, norepinephrine, and acetylcholine play a critical role in controlling the learning about the association between stimuli and actions and rewards and punishments, and also in regulating the way that networks process information and effect decisions. Precise characterization of at least one part of their function in these respects comes from theories originating in statistics, operations research, and engineering, and computational theory ties together neural, psychological, ethological, and even economic notions. ©2009 Elsevier Ltd All rights reserved.