Interaction plots are used frequently in psychology research to make inferences about moderation hypotheses. A common method of analyzing and displaying interactions is to create simple-slopes or marginal-effects plots using standard software programs. However, these plots omit features that are essential to both graphic integrity and statistical inference. For example, they often do not display all quantities of interest, omit information about uncertainty, or do not show the observed data underlying an interaction, and failure to include these features undermines the strength of the inferences that may be drawn from such displays. Here, we review the strengths and limitations of present practices in analyzing and visualizing interaction effects in psychology. We provide simulated examples of the conditions under which visual displays may lead to inappropriate inferences and introduce open-source software that provides optimized utilities for analyzing and visualizing interactions.