Combustion is the main source of energy and environmental pollution. The objective of the combustion study is to improve combustion efficiency and reduce pollution emissions. In the past decades, machine learning (ML), as a branch of artificial intelligence, has attracted increasing interests, especially in the combustion field. In the present work, the definition, current status and recent progress in the applications of ML on research related to combustion are briefly reviewed. Combustion studies combined with ML can be divided into theoretical and industrial aspects. Studies of combustion theory include CFD simulation, combustion phenomenon and fuel. ML is used to reduce the cost of CFD, including reducing the scale of combustion mechanism, saving the memory storage of the probability density function table and optimizing Large Eddy Simulation. ML helps in the research of combustion phenomena, such as detecting thermoacoustic combustion oscillation, portioning regimes of ignition and detonation, and reconstructing cellular surface of gaseous detonation. ML has been also applied to study physiciochemical properties of fuels and design the next generation fuels. In the industrial research with respect to combustion, ML is mainly applied to produce electricity and power by power plants or engines, and less to other fields. ML could figure out problems of combustion in various kinds of furnaces and post-combustion emissions in power plants. In addition, ML plays important roles in biodiesel engine, Homogenous Charge Compression Ignition (HCCI), and operation control or monitoring in the engines. Moreover, ML also applies to other industrial studies related to combustion, mainly to particulate matters. The methods of the mentioned studies were summarized in detail and the potential applications of ML in combustion community were proposed.