Stoves/burners are combustion appliances widely used for extraction/conversion of the energy of fuels for thermal purposes, heating, etc. Various types of stoves/burners have been discussed here for burning fossil/non-fossil fuels solid, liquid and gases. Energy-conserving models of stoves/burners have been presented here, with special reference to their thermal efficiencies. The information conveyed is important and useful for energy-saving and designing of thermally efficient combustion appliances. Accidents caused by the bursting of stoves have also been discussed. Several improved designs of household cooking-stoves have been evaluated and are discussed in this paper along with relevant safety measures.