We have been sensitized to children with high intellectual potential (HIP) having difficulties given the number of children consulting in our outpatient medico-psychological centres for scholastic problems (possibly leading to school failure), anxiety disorders or behavioral disorders such as attention deficit/hyperactivity disorder (ADHD), and in which a high intellectual potential was discovered during psychological assessments. It is the contrast, and more precisely the paradox, between the high intellectual potential of these children and their scholastic difficulties (including school failure), and the psychic suffering expressed by some of them, which led us to question, challenge and propose therapeutic and educational care adapted to these children. It is in this context that we created in December 2005 the CNAHP (National Center for Assistance to High Potential children and adolescents) which is a public centre integrated into the hospital-university department of child and adolescent psychiatry at Rennes. It is noteworthy that not all children with HIP have difficulties, and children with school failure or behavioral problems are not always children with HIP. However, it is necessary not to minimize the problem raised by children with HIP with difficulties by ignoring its frequency or by considering that these children are “intelligent” enough to manage by themselves and do not need to be helped, whereas some of them can show school failure and even be de-scholarized. Indeed, based on the definition of the World Health Organization (WHO) of an intellectual Quotient (IQ) above 130 (level corresponding to a statistical threshold), the frequency of children with HIP represents 2.3% of the population of schoolchildren aged 6 to 16. The frequency is therefore not so rare. However, it remains to be determined by French epidemiological studies what is the actual frequency of children with difficulties within a population of children with HIP. The analysis of the CNAHP research data from a clinical population (children with HIP consulting for difficulties) highlights that children with HIP can show major school problems (including school failure, defined here as having or foreseeing repetition of a grade), which corresponds to 7.5% of 611 children with HIP consulting at the CNAHP) and socioemotional problems (emotional regulation disorders) in relation to their high intellectual potential. In particular, anxiety disorders were the most frequent psychiatric disorders observed in this population (40.5%) and were significantly associated with high verbal potential. This significant association requires further studies to avoid establishing a simplistic unidirectional and reductive linear cause-effect relationships. Indeed, a high verbal potential can elicit and/or reinforce anxiety-producing representations, but anxiety disorders may also lead to a defensive over investment of verbal language. The results are discussed in this article and suggest that scholastic and/or psychological difficulties encountered by some children with HIP can be related to their high intellectual potential. It is necessary to develop therapeutic and educational care adapted to these children from a better understanding, based on research results, of their possible difficulties but also cognitive abilities. Even when children with HIP have scholastic and/or psychological difficulties, some of their cognitive skills can be preserved contrary to appearances, with for example, as seen in the CNAHP results, excellent attentional capacities shown by cognitive tests contrasting with behavioral attention deficit reported by parents. These skills are important to identify as they are resources which support the therapeutic and educational project. It is probably through an articulation among professionals from national education, health and research, in alliance with the family (parents, child, and siblings), that advances will be made. In the same way that professionals have been interested in children with intellectual disabilities, it is important to be concerned by children with HIP and difficulties located at the other end of the continuum. It is a question of ethics which concerns both caregivers and teachers. It is also a societal issue that concerns all of us given that the expression of high intellectual and creative potential in children may be essential to the societal development of innovative strategies and each nation's future. Finally, the discussion can be extended to all children, independent of their potential. What we learn from children with HIP and difficulties can be applied to each child: it is important at family, school and societal levels to facilitate the expression of the potential of children, to value their skills, and to help them to remove possible inhibitions of their potential based on individualized projects. The acceptance of singularity and differences in children can contribute to tolerance and the development of creativity, in the interest of the subject and of society.