Galaxy clusters are formed via nonlinear growth of primordial density fluctuations and are the most massive gravitationally bound objects in the present Universe. Their number density at different epochs and their properties depend strongly on the properties of dark matter and dark energy, making clusters a powerful tool for observational cosmology. Observations of the hot gas filling the gravitational potential well of a cluster allows studying gasdynamic and plasma effects and the effect of supermassive black holes on the heating and cooling of gas on cluster scales. The work of Yakov Borisovich Zeldovich has had a profound impact on virtually all cosmological and astrophysical studies of galaxy clusters, introducing concepts such as the Harrison?Zeldovich spectrum, the Zeldovich approximation, baryon acoustic peaks, and the Sunyaev?Zeldovich effect. Here, we review the most basic properties of clusters and their role in modern astrophysics and cosmology.