This paper reviews 47 articles dealing with tensions at the intersection of management control and innovation. One purpose is to present the status of the research in the area in terms of types of articles, research methods, theoretical approaches, and tension-related terms used. A second purpose is to conceptually compare the use and interpretations of tension in the reviewed articles, as well as to systematically map and categorize highlighted competing demands. A third purpose is to suggest a tension-based framework. Among other characteristics and trends, the paper indicates an increased research interest in the issue of tensions during the review period (1991–2015). Although different theoretical approaches are adopted, the contingency approach is the most common. Furthermore, the review shows that several tension-related terms are used either alone or in parallel in the articles, often interchangeably and without clarifying their definitions. The tension-based framework presents four different types of tension: (1) inherent innovation-control tensions, (2) inherent management control tensions, (3) created management control tensions, and (4) decision-making tensions in innovation practices. The framework also suggests interpretations of and responses to tensions related to management control and innovation. Theoretically, the framework can enable a more precise debate that builds on previous research, since it clarifies potential ways to structure future research. From a practical point of view the presented framework can be helpful for managers dealing with tensions, by encouraging creative management control solutions that can enable innovation.