Context: To accelerate time-to-market and improve customer satisfaction, software-producing organizations have adopted continuous delivery practices, impacting the relations between development and infrastructure professionals. Yet, no substantial literature has substantially tackled how the software industry structures the organization of development and infrastructure teams. Objective: In this study, we investigate how software-producing organizations structure their development and infrastructure teams, specifically how is the division of labor among these groups and how they interact. Method: After brainstorming with 7 DevOps experts to better formulate our research and procedures, we collected and analyzed data from 37 semi-structured interviews with IT professionals, following Grounded Theory guidelines. Results: After a careful analysis, we identified four common organizational structures: (1) siloed departments, (2) classical DevOps, (3) cross-functional teams, and (4) platform teams. We also observed that some companies are transitioning between these structures. Conclusion: The main contribution of this study is a theory in the form of a taxonomy that organizes the found structures along with their properties. This theory could guide researchers and practitioners to think about how to better structure development and infrastructure professionals in software-producing organizations.