To understand the essence of memory, one must examine the working of the brain on many levels. It is important to find the appropriate level to study the particular aspect of memory under investigation. In this review, I will focus on insights gained from examining memory at the molecular level. I will illustrate these insights with specific examples from examining the molecular and cellular mechanisms underlying long-term facilitation in the marine mollusk Aplysia and long-term potentiation, studied mainly in rodents. In particular, I will discuss how molecular memory traces are formed and focus in detail on what role increasing the level of proteins through protein synthesis and gene expression plays in memory formation. I will point out three important constraints from molecular work that should impact on cognitive modeling of the nervous system: (i) the induction of plasticity depends on the 'state' of the synapse; (ii) there are multiple independent molecular traces formed after experience with different half-lives; and (iii) the requirement for the conjunction of synaptic activation and new protein synthesis implies that new conjunctions are required to induce long-term memory formation.