We report on 35 years of research into behavior and ecology of the Australian sleepy lizard, Tiliqua rugosa. We describe the unusually long monogamous pairing period in this lizard before mating takes place each spring, and the long-term persistence of mating pairs, reforming each spring for up to 27 years. We review hypotheses, observations, and experiments and conclude that females drive the pairing, becoming more receptive to males that have provided prolonged attention, because of the advantages they gain through greater awareness of approaching danger. We suggest that long-term pair fidelity has resulted from a higher reproductive efficiency between familiar partners. We then consider the broader social network structure in the sleepy lizard population, suggesting from our analyses that lizards make more contacts with their neighbors, sometimes agonistically, than if they were moving at random. There are few kin-based associations in the networks, but lizards with different personality types have different network positions. The broad social structure of the population is robust to ecological and environmental changes, although various network parameters are adjusted with different climate or habitat conditions. The overall social structure of the sleepy lizard population has an important role in transmission of parasites and pathogens. Finally we consider why this species is one of the very few reptiles for which stable social living has been reported. This may be because reptile social living is relatively under studied. Alternatively, we suggest, many reptile species may be constrained from evolving social structures, because they lack either the necessary cognitive ability or a strong defense against the high risk of pathogen transmission that comes from social living.