Down syndrome (DS) is caused by the overexpression of genes on triplicated regions of human chromosome 21 (Hsa21). While the resulting physiological and behavioral phenotypes vary in their penetrance and severity, all individuals with DS have variable but significant levels of cognitive disability. At the core of cognitive processes is the phenomenon of synaptic plasticity, a functional change in the strength at points of communication between neurons. A wide variety of evidence from studies on DS individuals and mouse models of DS indicates that synaptic plasticity is adversely affected in human trisomy 21 and mouse segmental trisomy 16, respectively, an outcome that almost certainly extensively contributes to the cognitive impairments associated with DS. In this review, we will highlight some of the neurophysiological changes that we believe reduce the ability of trisomic neurons to undergo neuroplasticity-related adaptations. We will focus primarily on hippocampal networks which appear to be particularly impacted in DS and where consequently the majority of cellular and neuronal network research has been performed using DS animal models, in particular the Ts65Dn mouse. Finally, we will postulate on how altered plasticity may contribute to the DS cognitive disability.