Catalyst stability is one of the greatest challenges faced for the utilization of heterogeneous catalysts in the development of biomass conversion to chemicals and fuels. As many biomass transformations are performed in water, hydrothermal stability of supported metal catalysts is especially critical. This Review aims to increase attention on the hydrothermal stability of supported metal catalysts by looking at the stability of common catalyst supports, deactivation modes, and strategies to improve their durability. While common oxides such as silica, alumina, zeolite, and zirconia are not stable to hydrolytic attack, carbon, and titania show promising resistance. In addition to catalyst support leaching, amorphization, and collapse caused by hydrothermal conditions, supported metal catalysts can deactivate by sintering, leaching, poisoning, carbon deposition, and restructuring of the active metal sites. Several strategies are discussed to improve stability of supported metal catalysts: coating on the oxide, overcoating on the supported metal catalyst, metal–support interaction, embedding metal particles, bimetallic catalysts, reactor design and process optimization, and other methods. A fundamental understanding of liquid–solid interactions and deactivation mechanisms, as well as strategies to improve the catalyst durability will help to develop robust catalytic materials for the scale-up and further application of aqueous-phase biomass conversion processes.