The evaporation of sessile droplets is a fundamental scientific problem that is key to numerous physical and biological processes, including a wide range of industrial applications such as agrochemical spraying of plants, cooling technologies, desalination, DNA synthesis, ink-jet printing, painting, protein crystallography, and surface patterning, and, as a result, has been the subject of an explosion of analytical, experimental, and numerical investigations in recent years. However, despite its intrinsic complexity and multidisciplinary nature, considerable insight can be gained into many fascinating aspects of the problem, including the competition between multiple droplets and the evaporation of droplets in confined environments, by developing and solving a range of mathematical models.