From the traditional perspective of associative learning theory, the hypothesis linking modifications of synaptic transmission to learning and memory is plausible. It is less so from an information-processing perspective, in which learning is mediated by computations that make implicit commitments to physical and mathematical principles governing the domains where domain-specific cognitive mechanisms operate. We compare the properties of associative learning and memory to the properties of long-term potentiation, concluding that the properties of the latter do not explain the fundamental properties of the former. We briefly review the neuroscience of reinforcement learning, emphasizing the representational implications of the neuroscientific findings. We then review more extensively findings that confirm the existence of complex computations in three information-processing domains: probabilistic inference, the representation of uncertainty, and the representation of space. We argue for a change in the conceptual framework within which neuroscientists approach the study of learning mechanisms in the brain.