DevOps and continuous delivery have impacted the organizational structures of development and infrastructure groups in software-producing organizations. Our research aims at revealing the different options adopted by the software industry to organize such groups, understanding why different organizations adopt distinct structures, and discovering how organizations handle the drawbacks of each structure. We interviewed 68 carefully-selected IT professionals, 45 working in Brazil, 10 in the USA, 8 in Europe, 1 in Canada, and 4 in globally distributed teams. By analyzing these conversations through a Grounded Theory process, we identified conditions, causes, reasons to avoid, consequences, and contingencies related to each discovered structure (segregated departments, collaborative departments, API-mediated departments, and single department). In this way, we offer a theory to explain organizational structures for development and infrastructure professionals. This theory can support practitioners and researchers in comprehending and discussing the DevOps phenomenon and its related issues, and also provides valuable input to practitioners’ decision-making.