The current research study discusses and characterises the fire decay and cooling phase of post-flashover compartment fires, as they are often mixed up despite their important heat transfer differences. The two phases are defined according to the fire heat release rate time-history. The fire decay represents the phase in which the fire heat release rate decreases from the ventilation- or fuel-limited steady-state value of the fully-developed phase to fire extinguishment. This phase is highly influenced by the fuel characteristics, ranging from fast decays for hydrocarbon and liquid fuels to slow decays for charring cellulosic fuels (wood). Once the fuel is consumed, the compartment volume enters the cooling phase, where the cooling in the gas-phase and solid-phase happens with significantly different modes and characteristic times. The thermal boundary conditions at the structural elements are then defined according to physical characteristics and dynamics within the compartment. The research study also underlines how the existing performance-based methodologies lack explicit definitions of the decay and cooling phases and the corresponding thermal boundary conditions for the design of fire-safe structural elements under realistic fire conditions.