Combustion of fossil fuels has been continuously generating over 70% of the total energy for our human society, concurrently emitting vastly greenhouse gases and ecologically harmful pollutants. To mitigate the adverse issue, combustion technologies of a new type were successfully developed and debuted around 1990, associated with various terms of "flameless oxidation (FLOX)", "flameless combustion (FLC)", "high-temperature air combustion (HiTAC)", and "moderate and intense low-oxygen dilution (MILD) combustion". These combustion processes may be regarded as similar or the same class of combustion, because they all involve high preheat and deep dilution of individual reactants (nonpremixed) or the reactant mixture (premixed), prior to main combustion reactions, with high-temperature flue gases (burnt products) internally and/or externally. Very significantly, all of these combustion technologies can simultaneously achieve high efficiency and ultralow emissions of nitric oxides (NOx), light, and noise. This class of combustion has been frequently unified as "MILD combustion". Highly worthy to note, as a particular type of combustion, the MILD combustion has thus far been most extensively explored, resulting in many hundreds to 1000 academic articles published by various energy-related journals and conferences. The present review summarizes the research progress in the gaseous-fuel MILD combustion on its definition, ignition, evolution, and NOx emissions, specifically, through its aspects associated with open jet flames in hot coflow and industrial flames in combustion chamber or furnace. Also, discussions are provided on the relevant terminologies, existing problems, and further fundamental issues.