Long-term and short-term memories differ primarily in the duration of their retention. At a molecular level, long-term memory (LTM) is distinguished from short-term memory (STM) by its requirement for new gene expression. In addition to transcription (nuclear gene expression) the translation of stored mRNAs is necessary for LTM formation. The mechanisms and functions for temporal and spatial regulation of mRNAs required for LTM is a major contemporary problem, of interest from molecular, cell biological, neurobiological and clinical perspectives. This review discusses primary evidence in support for translational regulatory events involved in LTM and a model in which different phases of translation underlie distinct phases of consolidation of memories. However, it focuses largely on mechanisms of memory persistence and the role of prion-like domains in this defining aspect of long-term memory. We consider primary evidence for the concept that Cytoplasmic Polyadenylation Element Binding (CPEB) protein enables the persistence of formed memories by transforming in prion-like manner from a soluble monomeric state to a self-perpetuating and persistent polymeric translationally active state required for maintaining persistent synaptic plasticity. We further discuss prion-like domains prevalent on several other RNA-binding proteins involved in neuronal translational control underlying LTM. Growing evidence indicates that such RNA regulatory proteins are components of mRNP (RiboNucleoProtein) granules. In these proteins, prion-like domains, being intrinsically disordered, could mediate weak transient interactions that allow the assembly of RNP granules, a source of silenced mRNAs whose translation is necessary for LTM. We consider the structural bases for RNA granules formation as well as functions of disordered domains and discuss how these complicate the interpretation of existing experimental data relevant to general mechanisms by which prion-domain containing RBPs function in synapse specific plasticity underlying LTM.