Hydrogen (H) spillover in nonreducible oxides such as zeolites and Al₂O₃ has been a highly controversial phenomenon in heterogeneous catalysis. Since industrial catalysts are predominantly prepared using these materials as supports, it is important to understand the mechanism and catalytic functions of H spillover on their surfaces. In the past decade, fundamental studies on zeolite-encapsulated metal catalysts have revealed that H spillover and reverse spillover can be utilized in the design of hydrogenation and dehydrogenation catalysts with improved properties. Both experimental and theoretical studies have indicated that H spillover can occur in nonreducible oxides when they possess substantial acid sites that aid the surface migration of active H. In the present review, we will discuss the possible mechanisms of H spillover in nonreducible oxides and the unique opportunities of using this phenomenon for the design of advanced hydroprocessing catalysts.