Drug repurposing faces various challenges that can impede its success. We developed a framework outlining key challenges in drug repurposing to explore when and how health technology assessment (HTA) methods can address them. We identified 20 drug-repurposing challenges across the categories of data access, research and development, collaboration, business case, regulatory and legal challenges. Early incorporation of HTA methods, including literature review, empirical research, stakeholder consultation, health economic evaluation and uncertainty assessment, can help to address these challenges. HTA methods can assess the value proposition of repurposed drugs, inform further research and ultimately help to bring cost-effective repurposed drugs to patients.