The amount and availability of proteins are regulated by their synthesis, degradation, and transport. These processes can specifically, locally, and temporally regulate a protein or a population of proteins, thus affecting numerous biological processes in health and disease states. Accordingly, malfunction in the processes of protein turnover and localization underlies different neuronal diseases. However, as early as a century ago, it was recognized that there is a specific need for normal macromolecular synthesis in a specific fragment of the learning process, memory consolidation, which takes place minutes to hours following acquisition. Memory consolidation is the process by which fragile short-term memory is converted into stable long-term memory. It is accepted today that synaptic plasticity is a cellular mechanism of learning and memory processes. Interestingly, similar molecular mechanisms subserve both memory and synaptic plasticity consolidation. In this review, we survey the current view on the connection between memory consolidation processes and proteostasis, i.e., maintaining the protein contents at the neuron and the synapse. In addition, we describe the technical obstacles and possible new methods to determine neuronal proteostasis of synaptic function and better explain the process of memory and synaptic plasticity consolidation.