The rational of Low NOx Burners (LNB) and the processes which limit their performance are discussed. Information on the chemistry of combustion and nitrogen species interconversion serves as the guide for the temperature and mixing histories of the fuel to lead to minimum NOx emissions without excessive flame length. The tools required to achieve optimal distributed air admiring are those of fluid dynamics. Three examples are discussed: the LNB design in which air-fuel mixing near the burner is suppressed by radial density stratification but mixing is vigorous further downstream to ensure complete combustion; Gas Turbine Combustors with ultra-lean premixed flames in which flame stability close to the fuel-lean flammability limit and CO emission have to be reconciled with NOx emission; and Topping Combustors for coal fired Combined Gas Turbine-Steam Cycles in which the fuel-N bearing syngas and the cooling of the combustor walls by the high temperature combustion products of fluidized combustion of coal char present problems.