The Sustainable Development Goals (SDGs) aspire to “leave no-one behind”. Universal access to assistive products is a critical link between the realization of the SDGs and those most likely to be left behind. However, assistive technology provision in many countries, particularly low- and middle-income countries, has traditionally been conducted through small-scale local providers, manufacturing products of varying degrees of quality at a limited price range. An effective way to scale these production and provision enterprises to the required level is needed to close the gap between available and required assistive technology. We argue that better access to assistive technology will only be realized through the adoption of a far stronger systems thinking and market shaping approach. We undertook a rapid literature review to explore the relationship between market shaping and assistive technology. Based on our review, we present an emergent framework for conceptualizing intersections between systems thinking and market shaping for assistive technology—the SMART (Systems-Market for Assistive and Related Technologies) Thinking Matrix.