  Formation of dark matter halos is sensitive to the expansion rate of the
Universe and to the growth of structures under gravitational collapse.
Virialization of halos heats the gaseous intra-cluster medium to high
temperatures, leading to copious emission of photons at X-ray wavelengths. We
summarize the progress of X-ray surveys in determining cosmology using galaxy
clusters. We review recent cosmological results based on cluster volume
abundance, clustering, standard candles, extreme object statistics, and present
relevant theoretical considerations. We discuss clusters as gravitation theory
probes and present an outlook on future developments.
