Intuition is the ability to understand immediately without conscious reasoning and is sometimes explained as a 'gut feeling' about the rightness or wrongness of a person, place, situation, temporal episode or object. In contrast, insight is the capacity to gain accurate and a deep understanding of a problem and it is often associated with movement beyond existing paradigms. Examples include Darwin, Einstein and Freud's theories of natural selection, relativity, or the unconscious; respectively. Many cultures name these concepts and acknowledge their value, and insight is recognized as particularly characteristic of eminent achievements in the arts, sciences and politics. Considerable data suggests that these two concepts are more related than distinct, and that a more distributed intuitive network may feed into a predominately right hemispheric insight-based functional neuronal architecture. The preparation and incubation stages of insight may rely on the incorporation of domain-specific automatized expertise schema associated with intuition. In this manuscript the neural networks associated with intuition and insight are reviewed. Case studies of anomalous subjects with ability-achievement discrepancies are summarized. This theoretical review proposes the prospect that atypical localization of cognitive modules may enhance intuitive and insightful functions and thereby explain individual achievement beyond that expected by conventionally measured intelligence tests. A model and theory of intuition and insight's neuroanatomical basis is proposed which could be used as a starting point for future research and better understanding of the nature of these two distinctly human and highly complex poorly understood abilities.