In recent years, advances in experimental techniques have allowed for the first time simultaneous measurements of many interacting components in living systems at almost all scales, making now an exciting time to search for physical principles of collective behavior in living systems. This thesis focuses on statistical physics approaches to collective behavior in networks of interconnected neurons; both statistical inference methods driven by real data, and analytical methods probing the theory of emergent behavior, are discussed. Chapter 3 is based on work with F. Randi, A. M. Leifer, and W. Bialek [Chen et al., 2019], where we constructed a joint probability model for the neural activity of the nematode, Caenorhabditis elegans. In particular, we extended the pairwise maximum entropy model, a statistical physics approach to consistently infer distributions from data that has successfully described the activity of networks with spiking neurons, to this very different system with neurons exhibiting graded potential. We discuss signatures of collective behavior found in the inferred models. Chapter 4 is based on work with W. Bialek [Chen and Bialek, 2020], where we examine the tuning condition for the connection matrix among neurons such that the resulting dynamics exhibit long time scales. Starting from the simplest case of random symmetric connections, we combine maximum entropy and random matrix theory methods to explore the constraints required from long time scales to become generic. We argue that a single long time scale can emerge generically from realistic constraints, but a full spectrum of slow modes requires more tuning.