Structure is widely acknowledged to be important for the function of ribonucleic acids (RNAs) and proteins. However, due to the relative accessibility of sequence information compared to structure information, most large genomics studies currently use only sequence-based annotation tools to analyze the function of expressed molecules. In this thesis, I introduce two novel computational methods for genome-scale structure-function analysis and demonstrate their application to identifying RNA and protein structures involved in synaptic plasticity and potentiation—important neuronal processes that are thought to form the basis of learning and memory. First, I describe a new method for de novo identification of RNA secondary structure motifs enriched in co-regulated transcripts. I show that this method can accurately identify secondary structure motifs that recur across three or more transcripts in the input set with an average recall of 0.80 and precision of 0.98. Second, I describe a tool for predicting protein structural fold from amino acid sequence, which achieves greater than 96% accuracy on benchmarks and can be used to predict protein function and identify new structural folds. Importantly, both of these tools scale linearly with increasing numbers of input sequences, making them feasible to run on thousands of sequences at a time. Finally, I use these tools to investigate RNA localization and local translation in dendrites—two processes that are prerequisites for long-lasting synaptic potentiation. Using soma- and dendrite-specific RNA-sequencing data as a starting point, I define the full set of RNAs localized to the dendrites, identify novel secondary structure motifs enriched in these RNAs that may act as dendritic localization signals, and predict the structure of all proteins that would be produced by these localized RNAs during local translation. The results shed new light on potential regulatory mechanisms of dendritic localization and roles of locally translated proteins at the synapse, and demonstrate the utility of structure-based tools in genomics analysis.