Burners are mechanical elements that warrant heat production from combustion by ensuring a mixture between a fuel (gaseous, liquid, or solid) and oxidizer (generally air, naturally containing oxygen) or injecting a premixed fuel-oxidizer mixture. Generally, burners consist of one or multiple injectors resistant to high temperatures so that the mixture is ignited as soon as it leaves injectors. The mixing process requires the best regulation such that combustion efficiency is maximum with low unburnt and pollutants. The ignition process can be operated directly (stove burner, water heater, boiler, oven, etc.), or indirectly, for example, to produce mechanical work in a heat engine. Numerous parameters can be used to classify burners, among them fluid flow regime, injection direction, reactants mixture, and combustion process. According to the injection process, burners can be classified into two categories: premixed and nonpremixed injection. In premixed burners, fuel and oxidizer are well mixed before injection and ignition, whereas, in the second category, fuel and oxidizer are injected separately and then mixed in the burner or combustion chamber before ignition. According to flow dynamics, burners can be operated in a laminar or turbulent regime; however, laminar burners are almost limited to research purposes. Nearly all combustion applications use turbulent burners. When the fuel and oxidizer (or their mixture) are injected in the same direction, the burner is said “coflow burner,” whereas when they are injected in opposite directions, the burner is classified as a “counterflow burner.” Premixed burners have the best efficiencies and less unburnt, and they also permit accurate temperature and emissions control. Despite all these advantages, premixed burners are not safe, as flashback can easily occur in these burners. On the other hand, nonpremixed burners are fully safe since reactants are separated before ignition. Here, we will deal with coflow and counterflow burners in the flameless combustion (FC) process. Coflow burners received more attention since they have simple geometries and can be operated easily with varying different parameters of interest. On the other hand, counterflow burners are generally laminar and are used in fundamental researches. In the following, several burners operated under FC and especially moderate or intense low-oxygen dilution (MILD) combustion will be described; furthermore, results obtained using these burners are summarized. Two main sections are dedicated to the coflow and counterflow burners. Every section presents different types of burners used by researchers to investigate characteristics of combustion occurring in this kind of burners.