Down syndrome (DS), also known as trisomy 21, is a genetic disorder caused by triplication of Chromosome 21. Gene triplication may compromise different body functions but invariably impairs intellectual abilities starting from infancy. Moreover, after the fourth decade of life people with DS are likely to develop Alzheimer’s disease. Neurogenesis impairment during fetal life stages and dendritic pathology emerging in early infancy are thought to be key determinants of alterations in brain functioning in DS. Although the progressive improvement in medical care has led to a notable increase in life expectancy for people with DS, there are currently no treatments for intellectual disability. Increasing evidence in mouse models of DS reveals that pharmacological interventions in the embryonic and neonatal periods may greatly benefit brain development and cognitive performance. The most striking results have been obtained with pharmacotherapies during embryonic life stages, indicating that it is possible to pharmacologically rescue the severe neurodevelopmental defects linked to the trisomic condition. These findings provide hope that similar benefits may be possible for people with DS. This review summarizes current knowledge regarding (i) the scope and timeline of neurogenesis (and dendritic) alterations in DS, in order to delineate suitable windows for treatment; (ii) the role of triplicated genes that are most likely to be the key determinants of these alterations, in order to highlight possible therapeutic targets; and (iii) prenatal and neonatal treatments that have proved to be effective in mouse models, in order to rationalize the choice of treatment for human application. Based on this body of evidence we will discuss prospects and challenges for fetal therapy in individuals with DS as a potential means of drastically counteracting the deleterious effects of gene triplication.