To survive in today’s increasingly complex business environments, firms must embrace strategic paradoxes: contradictory yet interrelated objectives that persist over time. This can be one of toughest of all leadership challenges, as managers must accept inconsistency and contradictions. In this article, we develop and empirically test a set of hypotheses related to ambidexterity, a key example of a paradoxical strategy. Through our analysis of data from a survey of executive leaders, we find a link between organizational ambidexterity and strategic planning, suggesting that the complexities of navigating in explorative ventures require more explicit strategy work than the old certainties of a legacy business. We identify and discuss inherent paradoxes and their implications for firm performance in 22 industry-specific strategies, where empirical industry data shows a pattern of conflict between explorative growth strategies and exploitative profit strategies. We argue that this is just one of the inherent paradoxes in the ambidexterity construct.