As we cross the 2030 deadline to achieve the Sustainable Development Goals (SDGs), there is a growing sense of urgency around the need to accelerate the necessary transformations. These encompass a broad range of systems and require fundamental changes in system goals and design. In this paper, we undertake a narrative review of the literature relating to the acceleration of transformations and offer a framework for unlocking and accelerating transformations to the SDGs. While there is no blueprint for acceleration, there is an expanding knowledge base on important dynamics, impediments and enabling conditions across diverse literatures which can help to inform strategic interventions by actors. The emerging literature on positive tipping points and deep leverage points identifies opportunities to rewire systems design so that important system feedbacks create the conditions for acceleration. Transformation takes time and actors will need to build momentum to reorient systems around new goals, informed by knowledge of common policy, technology and behavioural feedbacks that govern system dynamics. Where resistance is strong, actors can seek to augment system design in ways that weaken balancing feedbacks that stabilise existing system configurations and strengthen reinforcing feedbacks that promote emerging system configurations oriented towards the SDGs. Well-designed and sequenced interventions can promote innovation and behaviour change and build and maintain political support. This can build critical enabling conditions and push systems towards large-scale tipping points, paving the way for decisive policy action that is crucial for triggering acceleration. We conclude by highlighting gaps and priorities for further research.