Creativity is a cornerstone of what makes us human, yet the neural mechanisms underlying creative thinking are poorly understood. A recent surge of interest into the neural underpinnings of creative behavior has produced a banquet of data that is tantalizing but, considered as a whole, deeply self-contradictory. We review the emerging literature and take stock of several long-standing theories and widely held beliefs about creativity. A total of 72 experiments, reported in 63 articles, make up the core of the review. They broadly fall into 3 categories: divergent thinking, artistic creativity, and insight. Electroencephalographic studies of divergent thinking yield highly variegated results. Neuroimaging studies of this paradigm also indicate no reliable changes above and beyond diffuse prefrontal activation. These findings call into question the usefulness of the divergent thinking construct in the search for the neural basis of creativity. A similarly inconclusive picture emerges for studies of artistic performance, except that this paradigm also often yields activation of motor and temporoparietal regions. Neuroelectric and imaging studies of insight are more consistent, reflecting changes in anterior cingulate cortex and prefrontal areas. Taken together, creative thinking does not appear to critically depend on any single mental process or brain region, and it is not especially associated with right brains, defocused attention, low arousal, or alpha synchronization, as sometimes hypothesized. To make creativity tractable in the brain, it must be further subdivided into different types that can be meaningfully associated with specific neurocognitive processes.