Predictive modelling of compartment fires remains very challenging, due to the prohibitively wide spectrum of scales to be resolved in simulations of turbulent flames and two-way coupling of gas-phase combustion with gasification of combustible material. This project will advance both problems by developing, from revisited theory, a novel 'sub-grid combustion model' (SCM) for un-resolved gas-phase combustion phenomena in large-eddy simulations (LES). The SCM will be capable of capturing flame extinction and (re-)ignition accurately, enabling prediction of these critical transient phenomena in fires by inclusion of finite-rate chemistry. The novel SCM will be implemented in multiple software packages and validated against available experimental data. Its advantage over conventional models (infinitely fast chemistry) will be demonstrated. The SCM will be tested in a systematic manner for unconfined flames, and then applied to predict transient development of under-ventilated enclosure fires. With respect to the latter, dynamics of flame spread and rapid increase of burning rate will be thoroughly examined. While advancing the problem of gas-solid coupling, both charring and non-charring combustible materials together with complex and combined heat and mass transfer will be considered, and finite-rate chemistry effects in flaming combustion will be investigated. A new approach for production of toxic species (CO) in under-ventilated fires will be developed and validated.