During learning, repetitive neuronal activity, or lack of it, causes strengthening or weakening, respectively, of specific synaptic connections between axons and dendrites. This process of remodelling synapses is known as synaptic plasticity and forms the cellular and molecular basis of memory and learning. It has been known for over 50 years that long-term plasticity requires new protein synthesis immediately after the learning stimulus. Clearly, a rapid local translational response must depend upon the availability of specific RNAs at the synapse. However, how most mRNAs are directed to the synapse is poorly understood, as is the mechanism by which synaptic RNA abundance is regulated. We have been systematically characterising the distributions of several hundred randomly chosen mRNAs as well as their rates of synthesis and decay near synapses using the powerful Drosophila neuromuscular model junction (NMJ) system. We find that approximately 10% of individual types of RNA present in neurones are located at the tips of synapses and in some cases we have shown that they encode proteins required for synaptic plasticity. Our genome wide analysis of RNA stability has identified a wide variation in cytoplasmic stability and in some cases we show that regulating stability determines the distribution of RNA across different cell types in the nervous system.