  The Sunyaev-Zel'dovich 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.
