Platform chemicals, also known as chemical building blocks, are substances that serve as starting materials for the synthesis of various value-added products, which find a wide range of applications. These chemicals are the key ingredients for many fine and specialty chemicals. Most of the transformations of platform chemicals are catalytic processes, which should meet the requirements of sustainable chemistry: to be not toxic for humans, to be safe for the environment, and to allow multiple reuses of catalytic materials. This paper presents an overview of a new class of heterogeneous catalysts based on nanoparticles of catalytically active metals stabilized by a polymer matrix of hypercrosslinked polystyrene (HPS). This polymeric support is characterized by hierarchical porosity (including meso- and macropores along with micropores), which is important both for the formation of metal nanoparticles and for efficient mass transfer of reactants. The influence of key parameters such as the morphology of nanoparticles (bimetallic versus monometallic) and the presence of functional groups in the polymer matrix on the catalytic properties is considered. Emphasis is placed on the use of this class of heterogeneous catalysts for the conversion of plant polysaccharides into polyols (sorbitol, mannitol, and glycols), hydrogenation of levulinic acid, furfural, oxidation of disaccharides, and some other reactions that might be useful for large-scale industrial processes that aim to be sustainable. Some challenges related to the use of HPS-based catalysts are addressed and multiple perspectives are discussed.