Graph theory has provided a powerful modeling foundation for problems in many domains, but we argue that group interactionsare better modeled by hypergraphs. As we work toward scalable systems for such hypergraph analysis, several major challenges and opportunities arise; here we highlight a sample of those challenges. We consider the need for efficient representations of hypergraphs, and show that in some cases it is possible to exploit the specific structure of a hypergraph to reduce storage overhead. We also explore several challenges in distributing computation on hypergraphs, including the need for more general partitioning approaches. Finally, we discuss several other problems that arise as we move from graphs to hypergraphs, including designing programming models, using hypergraphs to model real-world groups, and the need for a better understanding of the structural characteristics of hypergraphs.