The evaporation of droplets plays an important role in numerous natural and artificial processes. The conditions under which the droplet of water or other liquid evaporates can be divided into two significantly different large groups. The first group includes the evaporation of small spherical droplets suspended in a gas (e.g. atmospheric air) and evaporating before contact with solid surfaces. Such droplets can usually be considered isothermal and the liquid in the droplet can be assumed to be motionless. To the second group, we refer, as a rule, to larger droplets, the evaporation of which takes place or continues on a solid surface. The shape of these sessile droplets is usually far from spherical, depends on the droplet size and surface material properties, and changes with evaporation. At the beginning of evaporation the temperature field in such droplets is essentially inhomogeneous and, in addition, it can be necessary to account for the complex flow of liquid in the volume of the droplet.

Significant differences between the evaporation conditions of droplets suspended in a gas and those on a solid surface prompted the authors to separate two main sections of the review. At the beginning of each section, natural phenomena and various applications of the evaporating droplets are mentioned. The impressive pattern of a dry trace left by a dried droplet of human blood is presented.

The list of nine research topics for future work on evaporating airborne and sessile droplets is provided in the last section of the paper. The relevant literature is given for these potential research topics.