A fundamental problem of modelling combustion in fires stems from the enormous disparity in spatial scales to be replicated, from the sizes of fire plumes, compartments, and buildings, down to the microscopic scales at which chemical reactions of fuel oxidation occur. Current practice of fire modelling assumes reactions to be infinitely fast and controlled by reactant mixing, with the mixing rate modelled as in fully developed turbulence. These assumptions neither enable the consideration of critical phenomena of flame extinction and re-ignition, nor prediction of toxic combustion products (carbon monoxide). Conventional combustion models originally developed for high-velocity flames in furnaces, gas turbines, engines, are not based on the characteristics of low-velocity fire-driven buoyant flames. This PhD research addresses these fundamental problems and aims at developing a novel combustion model for large eddy simulations of buoyant flames, with the finite-rate chemistry accounted for. This model, designed to reconstruct the impact of the reactive diffusion flamelets at the sub-grid level, will be validated and applied to predict the structure, transient dynamics, and extinction of unconfined and enclosed fires. The effects of finite-rate chemistry on oscillatory combustion in under-ventilated enclosures and on formation and stability of “ghosting” flames will be investigated, and a method to predict CO production in under-ventilated fires will be developed and validated.