Experience triggers molecular cascades in organisms (learning) that lead to alterations (memory) to allow the organism to change its behavior based on experience. Understanding the molecular mechanisms underlying memory, particularly in the nervous system of animals, has been an exciting scientific challenge for neuroscience. We review what is known about forms of neuronal plasticity that underlie memory highlighting important issues in the field: (1) the importance of being able to measure how neurons are activated during learning to identify the form of plasticity that underlies memory, (2) the many distinct forms of plasticity important for memories that naturally decay both within and between organisms, and (3) unifying principles underlying the formation and maintenance of long-term memories. Overall, the diversity of molecular mechanisms underlying memories that naturally decay contrasts with more unified molecular mechanisms implicated in long-lasting changes. Despite many advances, important questions remain as to which mechanisms of neuronal plasticity underlie memory.