This article reviews the literature and explores the institutional and systemic factors that help and/or hinder change and innovation across school systems, with a focus on evidence from England. A number of authors have argued that schools and school systems need to become more innovative and adaptive if they are to meet the needs of 21st-century societies and economies. Quasi-market models premised on school autonomy, parental choice and vertical accountability have been seen as the best way to secure innovation, but the evidence of success remains thin. The article analyses four examples of change and finds that system-wide change is possible, but requires strong and sustained political support and capacity building within a values-based framework that allows for local agency and adaptation. It concludes by drawing out three implications: the need to prioritise ‘professional’ as well as ‘structural’ autonomy; the potential for vertical accountability frameworks to condition the ways in which parents perceive and value innovation; and the need to enhance the legitimacy of innovation in the eyes of education’s key stakeholders.