Several recent epidemiological studies attempted to identify risk factors for Alzheimer’s disease. Age, family history, genetic factors (APOE genotype, trisomy 21), physical activity, and a low level of schooling are significant risk factors. In this review, we summarize the known psychosocial risk factors for the development of Alzheimer’s disease in patients with Down syndrome and their association with neuroanatomical changes in the brains of people with Down syndrome. We completed a comprehensive review of the literature on PubMed, Google Scholar, and Web of Science about psychosocial risk factors for Alzheimer’s disease, for Alzheimer’s disease in Down syndrome, and Alzheimer’s disease in Down syndrome and their association with neuroanatomical changes in the brains of people with Down syndrome. Alzheimer’s disease causes early pathological changes in individuals with Down syndrome, especially in the hippocampus and corpus callosum. People with Down syndrome living with dementia showed reduced volumes of brain areas affected by Alzheimer’s disease as the hippocampus and corpus callosum in association with cognitive decline. These changes occur with increasing age, and the presence or absence of psychosocial risk factors impacts the degree of cognitive function. Correlating Alzheimer’s disease biomarkers in Down syndrome and cognitive function scores while considering the effect of psychosocial risk factors helps us identify the mechanisms leading to Alzheimer’s disease at an early age. Also, this approach enables us to create more sensitive and relevant clinical, memory, and reasoning assessments for people with Down syndrome.