Multifunctional catalysts have received considerable attention in the cascade reactions of biomass processing. A cascade (or tandem) reaction is realized when multiple reaction steps that require different catalysts are performed in a one-step process. These reactions require bi- or multifunctional catalysts or catalyst mixtures to serve successfully at each reaction step. In this review article, we discuss the major factors of the catalyst design influencing the structure–property relationships, which could differ depending on the catalyst type. The major factors include the amounts and strengths of acidic and basic sites, interactions between those and metal sites, synergetic effects, nanoparticle sizes and morphology, nanostructures, porosity, etc. The catalysts described in this review are based on zeolites, mesoporous solids, MOFs, and enzymes. The importance of continuous cascade processes is also examined.