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Besides gas molecules, the Earth's atmosphere contains condensed-phase particles, whose sizes range from a few nanometers to hundreds of micrometers. Some of these aerosol particles are visible in the form of smoke, dust, haze or cloud droplets, which are large enough to directly scatter and absorb light. The vast majority, however, need to be observed by other means. Atmospheric aerosol particles, including cloud droplets and ice crystals, are in constant interaction with the each other, gas-phase molecules and the surrounding environment. Many of these interactions are highly non-linear, multi-scale phenomena that involve a large number of different molecular species. While the complex processes governing the evolution of atmospheric aerosol and clouds are challenging to describe, their improved numerical prediction is necessary because of the important role aerosols and clouds play in the climate system and for air quality. In the past decades, notable steps forward have been taken both in terms of better empirical characterization of aerosol particles and clouds as well s their numerical prediction - and more important developments are in the horizon. In my presentation, I will present some of these past developments and their importance for air quality and climate projection, as well as highlight some recent results from the research forefront.