With the growing demand for low-carbon alternative fuels, natural gas (primarily methane) has emerged as a clean and reliable option. Catalytic combustion of methane, due to its occurrence at lower temperatures and significant reduction in pollutants such as NOx and CO, serves as an efficient alternative to conventional thermal combustion. This article provides a targeted review of heterogeneous catalytic supports used in this process. Initially, common supports, including carbon-based and ceramic-based materials, were systematically examined. The primary focus was on gamma-alumina as the most widely used industrial support, which, despite its high specific surface area and suitable stability, undergoes sintering, loss of surface area, and phase transition from γ to α at elevated temperatures, severely impairing catalyst performance. Deactivation factors and their mechanisms were analyzed, with impurity doping identified as the most effective strategy for enhancing thermal stability, preserving porosity, and delaying phase transition. Numerous studies demonstrate that targeted impurity doping not only increases the thermal stability of gamma-alumina beyond 1200 °C but also, by maintaining specific surface area and porous structure, enables the design of industrial catalysts with more stable performance and extended lifespan in the complete catalytic combustion of methane.