Down’s syndrome (DS) is the most frequent genetic cause of intellectual disability and patients with DS show significant psychopathology (18–23%). Moreover, individuals with DS often show a cognitive decline associated with ageing characterized by a deterioration in memory, language and cognitive functioning. According to these relevant findings, an overview is presented of state-of-the-art knowledge of the neurocognitive, neurobiological and psychopathological profile, assessment and treatment of patients with DS. The linguistic characteristics of DS develop differently along distinct developmental trajectories. Thus, for example, morphosyntax deficit, especially in production, is more evident in adolescence than in early childhood and lexicon is usually better preserved in all ages (at least in comprehension). So far, rehabilitation is the only effective approach for improving cognitive and linguistic abilities. However, ongoing preliminary reports on other approaches such as transmagnetic stimulation or drugs suggest alternative or integrative treatment for the future. Individuals with DS show typical organization of brain structures related to some cognitive abilities, such as reduced volume in frontal and prefrontal areas, which is related to poor executive and linguistic abilities. They also frequently show psychiatric disorders such as externalizing disorders as well as depression, anxiety and obsessive-compulsive disorder. Nevertheless, as for other genetic syndrome with intellectual disability, there is a significant lack of research specifically focused on treatments of psychiatric and behavioural problems in DS. This is true both for psychosocial and for pharmacological interventions.