There are many aspects of social, colonial, and individual behavior that are puzzling and difficult to understand. Mathematical models provide an ideal tool for understanding the possible behaviors of systems under different hypotheses, often providing surprising insights about the actual effects of different model pieces. We use a number of different types of theoretical, mathematical and computational models to examine a few areas of insect and social behavior related to cooperation. First we consider a self-organized storage pattern in the comb of honey-bees. This pattern makes the colony more efficient and helps facilitate the survival and normal development of the brood (young bees). We explore how the colony level patterns can emerge and be maintained by thousands of bees performing tasks using simple rules that rely only on local information. We discuss how the results of these models demonstrate gaps in the current knowledge of honey bee behavior and motivate further research on queen movement patterns. We then explore the evolution of restraint for the parasitoid wasp Hyposoter horticola, which parasitizes host egg clusters but utilizes only 30% of the eggs in each cluster. Since natural selection favors individuals with more offspring, it is puzzling that these wasps do not use more of the available resources. We use both theoretical models and empirical results to explore several plausible explanations for this behavior. We first consider whether the wasp's parasitism is reduced by physical/physiological constraints. Then, we explore selective pres- sures that might favor submaximal parasitism behavior and discuss the most reasonable explanation for sub-maximal parasitism by H. horticola. Last, we explore the related, but more general question of the evolution of cooperative behaviors. We use the iterated prisoner's dilemma to model the benefits and costs of cooperation for repeated interactions. We classify the population dynamics for interacting strategies to understand the conditions that favor greater levels of cooperation. We then explore the bifurcations of the system. These bifurcations show where small changes to parameter values produce qualitatively (and sometimes drastically) different population dynamics.