Efficient transformation of biomass to value-added chemicals and high-energy density fuels is pivotal for a more sustainable economy and carbon-neutral society. In this framework, developing potential cascade chemical processes using functionalised heterogeneous catalysts is essential because of their versatile roles towards viable biomass valorisation. Advances in materials science and catalysis have provided several innovative strategies for the design of new appealing catalytic materials with well-defined structures and special characteristics. Promising catalytic materials that have paved the way for exciting scientific breakthroughs in biomass upgrading are carbon materials, metal-organic frameworks, solid phase ionic liquids, and magnetic iron oxides. These fascinating catalysts offer unique possibilities to accommodate adequate amounts of acid-base and redox functional species, hence enabling various biomass conversion reactions in a one-pot way. This review therefore aims to provide a comprehensive account of the most significant advances in the development of functionalised heterogeneous catalysts for efficient biomass upgrading. In addition, this review highlights important progress ensued in tailoring the immobilisation of desirable functional groups on particular sites of the above-listed materials, while critically discussing the role of consequent properties on cascade reactions as well as on other vital processes within the bio-refinery. Current challenges and future opportunities towards a rational design of novel functionalised heterogeneous catalysts for sustainable biomass valorisation are also emphasized.