The Sunyaev-Zeldovich effect (SZE) provides a powerful tool for cosmological studies. Through recent advances in instrumentation and observational techniques it is now possible to obtain high quality measurements of the effect toward galaxy clusters. The analysis of the SZE toward a few tens of clusters has already led to interesting constraints on the Hubble constant and the mass density of the universe. In the near future, instruments exploiting the redshift independence of the SZE will be used to conduct deep surveys for galaxy clusters providing detailed information on the growth of large scale structure, tests of cosmological models and tight constraints on the cosmological parameters that describe our universe. In this review we provide an overview of the SZE and its use for cosmological studies. We summarize the current state of observations and the constraints on cosmological parameters already obtained and we discuss the power of using the SZE for future deep cluster surveys.
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