Tetrameric AMPA-type ionotropic glutamate receptors are primary transducers of fast excitatory synaptic transmission in the central nervous system, and their properties and abundance at the synaptic surface are crucial determinants of synaptic efficacy in neuronal communication across the brain. The induction of long-term potentiation (LTP) leads to the insertion of GluA1-containing AMPA receptors at the synaptic surface, whereas during long-term depression (LTD), these receptors are internalized into the cytoplasm of the spine. Disruptions in the trafficking of AMPA receptors to and from the synaptic surface attenuate both forms of synaptic plasticity. Homeostatic scaling up and scaling down, which are additional types of plasticity similar to LTP and LTD, are also regulated by the insertion and removal of GluA1-containing AMPA receptors from the synaptic surface. The trafficking of AMPA receptors is an intricate process assisted by various proteins. Furthermore, AMPA receptors are critical for the formation and consolidation of various types of memory, and alterations in their function are intimately associated with cognitive dysfunction in aging and several neurological and psychiatric diseases. In this review, we will provide an overview of the current understanding of how AMPA receptors regulate various forms of synaptic plasticity, their contribution to memory functions, and their role in aging and brain diseases.