Atomization and evaporation processes have extensively existed in a variety of scientific and engineering applications, such as, rain formation, spray cooling, and spray combustion in propulsion devices. In spray combustion, atomization and evaporation processes govern the resultant liquid droplet characteristics, which strongly affect the combustion efficiency and pollutant emissions. However, atomization and evaporation are very complicated processes that involve convoluted interfaces as well as the breakup and coalescence of liquid masses, together with mass and heat transfers on the interface. Deep insights into atomization and evaporation put a significant challenge to the measuring techniques due to the harsh conditions and multi-scale nature of the problem within the apparatus. With the developments of computational algorithm and computer capacity, detailed numerical simulation of the atomization and evaporation processes has been a promising tool to explore the underlying physics. Level set method is such an interface capturing method, and tremendous progresses have been made for detailed numerical simulation of atomization and evaporation over the past few decades. In this article, we attempt to review the recent progresses in the development of the level set method and its applications to atomization and evaporation. Firstly, the fundamentals of the level set method are introduced and recent advances in improving the mass conservation are emphasized. Secondly, numerical issues for detailed numerical simulation of atomization and evaporation are summarized and the strategies for treating them are highlighted. We then review the state-of-the-art progresses in detailed numerical simulation of atomization and evaporation with the level set method. The challenges and future prospects are summarized in the end. (C) 2019 The Authors. Published by Elsevier Ltd.