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In this paper we review the current problematic of high intelligence quotient (HIQ) individuals, as developed both in the paradigm of cognitive psychology and in that of clinical psychology. The evolution of the HIQ concept as well as that of intelligence models is presented. We insist on the limits of the cognitive approach alone, whereas clinical psychology highlights the particularities of these people, obliging us to widen the framework of HQI. As such, we prefer the notion of High Potential, underlining the fact that the processes involved are not only cognitive but general, therefore also emotional, affective, and creative. The comparison of the two paradigmatic approaches (cognitive psychology and clinical psychology) shows, particularly with regard to this theme, very different epistemological conceptions of intelligence. It also highlights the limits of neuropsychological tests in the face of the living, subtle, and embodied reality of differential psychology. These two approaches are both necessary and complementary.