This book chapter summarizes the new field of quantum catalysis and its application in the sustainable conversion of biomass into high-value products. It starts by outlining the pressing need for renewable resources and the critical role of catalysis in biomass valorization. The chapter discusses the fundamental quantum mechanical concepts for catalytic activity at the nanoscale, such as quantum confinement and tunneling. It presents basic quantum catalytic materials like quantum dots, carbon nanotubes, and graphene, highlighting their unique electronic and structural properties. Different biomass feedstocks and the wide range of value-added products available through quantum catalysis are discussed, with specific examples including the conversion of cellulose to 5-hydroxymethylfurfural (HMF) and its further oxidation to 2,5-furandicarboxylic acid (FDCA). The chapter also discusses the major roles of carbon nanotubes and graphene in improving the catalytic performance. Finally, the chapter presents the current challenges and proposes the future research directions in this promising area, with the revolutionary potential of quantum catalysis to achieve a sustainable bioeconomy.