People with Down syndrome (DS) virtually all develop intellectual disability (ID) of varying degree of severity, and also have a high risk of early Alzheimer's disease (AD). ID prior to the onset of dementia, and its relationship to the onset of dementia in DS is a complex phenomenon influenced by many factors, and scarcely understood. Unraveling the causative factors and modulators of these processes remains a challenge, with potential to be informative for both ID and AD, for the development of early biomarkers and/or therapeutic approaches. We review the potential relative and inter-connected roles of the chromosome 21 gene for amyloid precursor protein (APP), in both pathological conditions. Rare non-DS people with duplication of APP (dupAPP) get familial early onset AD (FEOAD) with virtually 100% penetrance and prominent cerebrovascular pathology, but don't suffer from ID before dementia onset. All of these features appear to be radically different in DS. On the other hand, rare individuals with partial trisomy 21 (T21) (with APP, but not DS-critical region in trisomy) have been described having ID. Likewise, partial T21 DS (without APP trisomy) show a range of ID, but no AD pathology. We review the multi-faceted roles of APP that might affect cognitive functioning. Given the fact that both Aβ secretion and synaptic maturation/plasticity are dependent on neuronal activity, we explore how this conflicting inter-dependency might affect cognitive pathogenesis in a dynamic way in DS, throughout the lifespan of an individual.