LES (Large Eddy Simulations) for turbulence is well established. In turbulent reacting flows, there is a range of options for the modelling of combustion and turbulence - chemistry interaction (TCI). A popular approach in fire simulations is EDC (Eddy Dissipation Concept). It is common practice to assume infinitely fast chemistry to date. However, a model for extinction is required then, which is typically based on temperature or enthalpy. In the present project, it is investigated whether the introduction of finite rate chemistry (FRC) in EDC can automatically predict extinction / re-ignition. Another advantage of the introduction of FRC is the potential of predicting minor species, which is interesting for toxicity, as well as for radiation modeling. Another approach for FRC is CMC (Conditional Moment Closure). However, ongoing research has revealed possible issues in correctly capturing the heat release rate, which is essential for extinction. This will be investigated and upon success, this can open up opportunities for the LES-CMC approach in fire simulations, due to the same potential of predicting minor species. The main focus in LES-CMC will be on the shape of the conditional scalar dissipation rate, combined with numerical aspects and grid spacing. Well-documented target test cases will include methanol pool fires, as well as methane, propane and ethylene flames (ranging from full burning to extinction). Radiation will be included in all simulations.