Medicine has conventionally had an individualist orientation to competence. Individual competence is conceptualized as a stable possession that, once acquired, holds across contexts. Individual competence is necessary; however, it is insufficient for quality health care. We also need to attend to collective competence in order to grapple with paradoxical truths about teamwork, such as: competent individuals can form incompetent teams. Collective competence is conceptualized as a distributed capacity of a system, an evolving, relational phenomenon that emerges from the resources and constraints of particular contexts. This article outlines a set of paradoxical truths about teamwork in health care and uses the concept of collective competence to explain how they can hold true. It then considers a set of persistent myths about teamwork which have their roots in an individualist orientation, exploring how they hold us back from meaningful change in how we educate for, and practice as, health care teams. Finally, the article briefly considers the implications of these truths and myths for educational issues such as interprofessional education and competency-based health professional education.