‘Grand challenges’ are gaining visibility in the policy agenda of most Member States of the Organisation for Economic Co-operation and Development (OECD). Diagnostic analysis, allowing identification of innovation systems problems and their causes, is needed in order to determine under what conditions public procurement of innovation (PPI) could contribute to the achievement of solutions for grand challenges. Based on a comprehensive review of the innovation policy literature, we propose an analytical framework in order to highlight how PPI can address three categories of failures: demand-side, supply-side, and user–supplier interaction failures. We use these categories as discriminating variables to define PPI ideal-types. Our PPI analytical framework allows us to define and link to each ideal-type elements of the PPI literature that focus on design (its characteristics and instruments). This provides a unified PPI framework which can contribute to better policymaking, evaluation, and analysis. In particular, the framework also allows to mobilise our PPI categories for a better conceptualisation of challenge-oriented policy more generally.