Clouds, which are common features in Earth's atmosphere, form in atmospheres of planets that orbit other stars than our Sun, in so-called extrasolar planets or exoplanets. Exoplanet atmospheres can be chemically extremely rich. Exoplanet clouds are therefore composed of a mix of materials that changes throughout the atmosphere. They affect atmospheres through element depletion and through absorption and scattering; hence, they have a profound impact on an atmosphere's energy budget. While astronomical observations point us to the presence of extrasolar clouds and make first suggestions on particle size and material composition, we require fundamental and complex modeling work to merge the individual observations into a coherent picture. Part of this work includes developing an understanding of cloud formation in nonterrestrial environments. ▪ Exoplanet atmospheres exhibit a wide chemical diversity that enables the formation of mineral clouds in contrast to the predominant water clouds on Earth. ▪ Clouds consume elements, causing specific atoms and molecules to drop in abundance. Transport processes such as gravitational settling or advection delocalize this process. ▪ Extrasolar planets can have extreme weather conditions where day- and nightside temperatures vary hugely. This affects cloud formation, and hence the cloud coverage and atmosphere's appearance can change dramatically. ▪ Dynamic extrasolar clouds develop intracloud lightning, and electric circuits may occur on more local, smaller scales in giant exoplanets compared to smaller, Earth-like planets with less dramatic hydrodynamics.