This article reviews and develops some theories about the neurobiological basis of creative innovation (CI). CI is defined as the ability to understand and express novel orderly relationships. A high level of general intelligence, domain-specific knowledge and special skills are necessary components of creativity. Specialized knowledge is stored in specific portions of the temporal and parietal lobes. Some anatomic studies suggest that talented people might have alterations of specific regions of the posterior neocortical architecture, but further systematic studies are needed. Intelligence, knowledge and special skills, however, are not sufficient for CI. Developing alternative solutions or divergent thinking has been posited to be a critical element of CI, and clinical as well as functional imaging studies suggest that the frontal lobes are important for these activities. The frontal lobes have strong connections with the polymodal and supramodal regions of the temporal and parietal lobes where concepts and knowledge are stored. These connections might selectively inhibit and activate portions of posterior neocortex and thus be important for developing alternative solutions. Although extensive knowledge and divergent thinking together are critical for creativity they alone are insufficient for allowing a person to find the thread that unites. Finding this thread might require the binding of different forms of knowledge, stored in separate cortical modules that have not been previously associated. Thus, CI might require the co-activation and communication between regions of the brain that ordinarily are not strongly connected. The observations that CI often occurs during levels of low arousal and that many people with depression are creative suggests that alterations of neurotransmitters such as norepinephrine might be important in CI. High levels of norepinephrine, produced by high rates of locus coeruleus firing, restrict the breadth of concept representations and increase the signal to noise ratio, but low levels of norepinephrine shift the brain toward intrinsic neuronal activation with an increase in the size of distributed concept representations and co-activation across modular networks. In addition to being important in divergent thinking, the frontal lobes are also the primary cortical region that controls the locus coeruleus-norepinephrine system. Thus creative people may be endowed with brains that are capable of storing extensive specialized knowledge in their temporoparietal cortex, be capable of frontal mediated divergent thinking and have a special ability to modulate the frontal lobe-locus coeruleus (norepinephrine) system, such that during creative innovation cerebral levels of norepinephrine diminish, leading to the discovery of novel orderly relationships.