Rule-based modeling is a powerful way to model kinetic interactions in biochemical systems. Rules enable a precise encoding of biochemical interactions at the resolution of sites within molecules, but obtaining an integrated global view from sets of rules remains challenging. Current automated approaches to rule visualization fail to address the complexity of interactions between rules, limiting either the types of rules that are allowed or the set of interactions that can be visualized simultaneously. There is a need for scalable visualization approaches that present the information encoded in rules in an intuitive and useful manner at different levels of detail. We have developed new automated approaches for visualizing both individual rules and complete rule-based models. We find that a more compact representation of an individual rule promotes promotes understanding the model assumptions underlying each rule. For global visualization of rule interactions, we have developed a method to synthesize a network of interactions between sites and processes from a rule-based model and then use a combination of user-defined and automated approaches to compress this network into a readable form. The resulting diagrams enable modelers to identify signaling motifs such as cascades, feedback loops, and feed-forward loops in complex models, as we demonstrate using several large-scale models. These capabilities are implemented within the BioNetGen framework but the approach is equally applicable to rule-based models specified in other formats.