The strength and efficiency of synaptic connections are affected by the environment or the experience of the individual. This property, called synaptic plasticity, is directly related to memory and learning processes and has been modeled at the cellular level. These types of cellular memory and learning models include specific stimulation protocols that generate a long-term strengthening of the synapses, called long-term potentiation, or a weakening of the said long-term synapses, called long-term depression. Although, for decades, researchers have believed that the main cause of the cognitive deficit that characterizes Alzheimer's disease (AD) and aging was the loss of neurons, the hypothesis of an imbalance in the cellular and molecular mechanisms of synaptic plasticity underlying this deficit is currently widely accepted. An understanding of the molecular and cellular changes underlying the process of synaptic plasticity during the development of AD and aging will direct future studies to specific targets, resulting in the development of much more efficient and specific therapeutic strategies. In this review, we classify, discuss, and describe the main findings related to changes in the neurophysiological mechanisms of synaptic plasticity in excitatory synapses underlying AD and aging. In addition, we suggest possible mechanisms in which aging can become a high-risk factor for the development of AD and how its development could be prevented or slowed.