Generating creative ideas and turning them into innovations is key for competitive advantage. However, endeavors toward creativity and innovation are bounded by constraints such as rules and regulations, deadlines, and scarce resources. The effect of constraints on creativity and innovation has attracted substantial interest across the fields of strategic management, entrepreneurship, industrial organization, technology and operations management, organizational behavior, and marketing. Research in these fields has focused on various constraints that trigger distinct mediating mechanisms but is fragmented and yields conflicting findings. We develop a taxonomy of constraints and mediating mechanisms and provide an integrative synthesis that explains how constraints affect creativity and innovation. Our review thus facilitates cross-disciplinary learning and sets the stage for further theoretical development.