Imprinted genes have been linked with diseases ranging from cancer, to metabolic syndromes, to psychiatric illness. With regard to psychiatric illness in particular, numerous lines of evidence, both from human and mouse studies, suggest imprinted genes affect behavior along with brain development and function. Nonetheless, the effect of imprinted genes on most complex traits is not well characterized. Moreover, the architecture of environment-by-imprinting effects is even less well-understood. The lack of characterization is likely due to the general difficulty of observing ``parent-of-origin effects'' (POEs), which typically arise in mammals from maternal effects--or from imprinting. To study POE/environment-by-POE, we can employ a relatively neglected but maximally powerful POE-detection system: the reciprocal cross (RX). Towards this end, we develop and apply computational methods for designing and analyzing RX experiments. Here, these techniques are applied in the context of RXs of inbred lines of mice, with a focus on behavior--but these techniques could be similarly employed in any model organism subject to POE, and on any complex trait. The first set of methods focuses on the analysis of expression and behavioral data from RXs of a single pair of classical inbred mouse strains, with offspring exposed in utero to various diets. In this analysis, we detected dozens of POE/diet-by-POE on gene expression, a handful of similar effects on behavior, and a possible connection between POE on expression and behavior. Motivated by these results, we engaged in a similar but larger study, the CC-POE, in which we RXd multiple pairs of inbred lines drawn from the Collaborative Cross (CC)--a panel of multiparental recombinant inbred mouse strains. To aid in the CC-POE design, we developed a novel method for selecting an optimal set of reciprocal crosses: the Reciprocal Cross Explorer. Finally, with the goal of analyzing CC-POE data, we develop a resource for variant imputation in the CC: the Inbred Strain Variant Database (available online at https://isvdb.unc.edu ). Taken together, methods developed in this dissertation represent progress towards a new way of studying POEs via RXs.