Recent progress on understanding the fundamental mechanisms governing droplet vaporization and combustion are reviewed. Topics include the classical d 2-Law and its limitations; the major transient processes of droplet heating and fuel vapor accumulation; effects due to variable transport property assumptions; combustion of multicomponent fuels including the miscible fuel blends, immiscible emulsions, and coal-oil mixtures, finite-rate kinetics leading to ignition and extinction; and droplet interaction. Potentially promising research topics are also suggested.