Social network analysis provides a broad and complex perspective on animal sociality that is widely applicable to almost any species. Recent applications demonstrate the utility of network analysis for advancing our understanding of the dynamics, selection pressures, development, and evolution of complex social systems. However, most studies of animal social networks rely primarily on a descriptive approach. To propel the field of animal social networks beyond exploratory analyses and to facilitate the integration of quantitative methods that allow for the testing of ecologically and evolutionarily relevant hypotheses, we review methodological and conceptual advances in network science, which are underutilized in studies of animal sociality. First, we highlight how the use of statistical modeling and triadic motifs analysis can advance our understanding of the processes that structure networks. Second, we discuss how the consideration of temporal changes and spatial constraints can shed light on the dynamics of social networks. Third, we consider how the study of variation at multiple scales can potentially transform our understanding of the structure and function of animal networks. We direct readers to analytical tools that facilitate the adoption of these new concepts and methods. Our goal is to provide behavioral ecologists with a toolbox of current methods that can stimulate novel insights into the ecological influences and evolutionary pressures structuring networks and advance our understanding of the proximate and ultimate processes that drive animal sociality.