Down syndrome (DS) is the leading cause of genetically-defined intellectual disability and congenital birth defects. Despite being one of the first genetic diseases identified, only recently, thanks to the phenotypic analysis of DS mouse genetic models, we have begun to understand how trisomy may impact cognitive function. Cognitive disabilities in DS appear to result mainly from two pathological processes: neurogenesis impairment and Alzheimer-like degeneration. In DS brain, suboptimal network architecture and altered synaptic communication arising from neurodevelopmental impairment are key determinants of cognitive defects. Hypocellularity and hypoplasia start at early developmental stages and likely depend upon impaired proliferation of neuronal precursors, resulting in reduction of numbers of neurons and synaptic contacts. The impairment of neuronal precursor proliferation extends to adult neurogenesis and may affect learning and memory. Neurodegenerative mechanisms also contribute to DS cognitive impairment. Early onset Alzheimer disease occurs with extremely high incidence in DS patients and is causally-related to overexpression of β-amyloid precursor protein (βAPP), which is one of the triplicated genes in DS. In this review, we will survey the available findings on neurodevelopmental and neurodegenerative changes occurring in DS throughout life. Moreover, we will discuss the potential mechanisms by which defects in neurogenesis and neurodegenerative processes lead to altered formation of neural circuits and impair cognitive function, in connection with findings on pharmacological treatments of potential benefit for DS.