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Nature-based solutions (NbS) are increasingly recognized as sustainable approaches to address societal challenges. Disaster risk reduction (DRR) has benefited by moving away from purely ‘grey’ infrastructure measures towards NbS. However, this shift also furthers an increasing trend of reliance on public acceptance to plan, implement and manage DRR measures. In this review, we examine how unique NbS characteristics relate to public acceptance through a comparison with grey measures, and we identify influential acceptance factors related to individuals, society, and DRR measures. Based on the review, we introduce the PA-NbS model that highlights the role of risk perception, trust, competing societal interests, and ecosystem services. Efforts to increase acceptance should focus on providing and promoting awareness of benefits combined with effective communication and collaboration. Further research is required to understand interconnections among identified factors and how they can be leveraged for the success and further uptake of NbS.