With the appearance of energy crisis, greenhouse effect, and heat management problem, the control especially the active and reversible control of heat transport or thermal conductivity is becoming urgent. However, phonon transport as controllable as electron transport has not yet been achieved. The difficulty lies in the lack of direct connection between phonons and external stimuli. To realize the goal of controllable phonon transport, a comprehensive and systematic understanding of thermal switching is essential. Consequently, we review recent progress and efforts on thermal switching in five different types of solid materials including ferroelectric materials, ferromagnetic materials, nanomaterials and nanostructures, polymers, and phase change materials, considering their thermal switching ability. Within each type of material, different controlling methods are reviewed and the underlying mechanisms are discussed, aimed at improving their thermal switching performance. Among the five types of solid materials, systematic comparison and analysis are provided, aimed at combining the advantages from different materials. In addition, current challenges and future perspectives are provided to highlight new and emerging research directions in this growing field.