Drug repurposing faces various challenges that 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. Based on 73 articles, an expert meeting, and seven semi-structured interviews, we identified 20 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 address these challenges. HTA methods can assess the value proposition of repurposed drugs, inform further research, and ultimately help bring cost-effective repurposed drugs to patients.