In the last decade, bioinformatic analyses of high-throughput proteomics and transcriptomics data have enabled researchers to gain insight into the molecular networks that may underlie lasting changes in synaptic efficacy. Development and utilization of these techniques have advanced the field of learning and memory significantly. It is now possible to move from the study of activity-dependent changes of a single protein to modeling entire network changes that require local protein synthesis. This data revolution has necessitated the development of alternative computational and statistical techniques to analyze and understand the patterns contained within. Thus, the focus of this review is to provide a synopsis of the journey and evolution toward big data techniques to address still unanswered questions regarding how synapses are modified to strengthen neuronal circuits. We first review the seminal studies that demonstrated the pivotal role played by local mRNA translation as the mechanism underlying the enhancement of enduring synaptic activity. In the interest of those who are new to the field, we provide a brief overview of molecular biology and biochemical techniques utilized for sample preparation to identify locally translated proteins using RNA sequencing and proteomics, as well as the computational approaches used to analyze these data. While many mRNAs have been identified, few have been shown to be locally synthesized. To this end, we review techniques currently being utilized to visualize new protein synthesis, a task that has proven to be the most difficult aspect of the field. Finally, we provide examples of future applications to test the physiological relevance of locally synthesized proteins identified by big data approaches.