Anxiety and depression are highly prevalent diseases with common heritable elements, but the particular genetic mechanisms and biological pathways underlying them are poorly understood. Part of the challenge in understanding the genetic basis of these disorders is that they are polygenic and often context-dependent. In my thesis, I apply a series of modern statistical tools to ascertain some of the myriad genetic and environmental factors that underlie fear-related behaviours in nearly two thousand heterogeneous stock mice, which serve as animal models of anxiety and depression. Using a Bayesian method called Sparse Partitioning and a frequentist method called Bagphenotype, I identify gene-by-sex interactions that contribute to variation in fear-related behaviours, such as those displayed in the elevated plus maze and the open field test, although I demonstrate that the contributions are generally small. Also using Bagphenotype, I identify hundreds of gene-by-environment interactions related to these traits. The interacting environmental covariates are diverse, ranging from experimenter to season of the year. With gene expression data from a brain structure associated with anxiety called the hippocampus, I generate modules of co-expressed genes and map them to the genome. Two of these modules were enriched for key nervous system components — one for dendritic spines, another for oligodendrocyte markers — but I was unable to find significant correlations between them and fear-related behaviours. Finally, I employed another Bayesian technique, Sparse Instrumental Variables, which takes advantage of conditional probabilities to identify hippocampus genes whose expression appears not just to be associated with variation in fear-related behaviours, but cause variation in those phenotypes.