A defining characteristic of the brain is its remarkable capacity to undergo activity-dependent functional and morphological remodelling via mechanisms of plasticity that form the basis of our capacity to encode and retain memories. Today, it is generally accepted that one key neurobiological mechanism underlying the formation of memories reside in activity-driven modifications of synaptic strength and structural remodelling of neural networks activated during learning. The discovery and detailed report of the phenomenon generally known as long-term potentiation, a long-lasting activity-dependent form of synaptic strengthening, opened a new chapter in the study of the neurobiological substrate of memory in the vertebrate brain, and this form of synaptic plasticity has now become the dominant model in the search for the cellular bases of learning and memory. To date, the key events in the cellular and molecular mechanisms underlying synaptic plasticity and memory formation are starting to be identified. They require the activation of specific receptors and of several molecular cascades to convert extracellular signals into persistent functional changes in neuronal connectivity. Accumulating evidence suggests that the rapid activation of neuronal gene programs is a key mechanism underlying the enduring modification of neural networks required for the laying down of memory. The recent developments in the search for the cellular and molecular mechanisms of memory storage are reviewed.