Facilitating team innovation is paramount to promoting progress in the science, technology, engineering, and math fields, as well as advancing national health, safety, prosperity, and welfare. However, innovation teams face a unique set of challenges due to the novelty and uncertainty that is core to the definition of innovation, as well as the paradoxical nature of idea generation and idea implementation processes. These and other challenges must be overcome for innovation teams to realize their full potential for producing change. The purpose of this review is, thus, to provide insight into the unique context that these teams function within and provide an integrative, evidence-based, and practically useful, organizing heuristic that focuses on the most important considerations for facilitating team innovation. Finally, we provide practical guidance for psychologists, organizations, practitioners, scientists, educators, policymakers, and others who employ teams to produce novel, innovative solutions to today’s problems.