A changing environment needs permanent adaptation, and adaptation requires both the memory of past events and cognitive transfer. Unfortunately, in spite of more than a century of research, cognitive transfer has not revealed all its secrets, especially in children. Intellectual disability adds even more complexity and obscures the understanding of what personal skills and environmental conditions must be for transfer to occur. Indeed deficits but also competencies coexist in individuals with intellectual disability. Concerning categorization, individuals with and without intellectual disability develop thoroughly in the same way in tasks that involve nonstrategic information processing, especially implicit and automatic processing. On the contrary intellectually-disabled people were often shown to encounter difficulties in the use of categorization in recall and recognition tasks, that is tasks involving attention and/or verbal processing of information. Yet memory strategies based on category usage may be relatively easily transferred by such people provided they are trained in these strategies. We present two studies with children and adolescents having slight intellectual disabilities, showing not only that strategy transfer is possible but also that two quite different trainings are valuable. We discussed the cognitive abilities concerned as well as the nature of training and the question of whether one must tend to adapt people to environment or environment to people.