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Analysis of the Sunyaev-Zel'dovich effect (SZE) and X-ray data provides a method of directly determining distances to galaxy clusters at any redshift. Clusters of galaxies contain hot (kB Te approx 10 keV) gas, known as the intracluster medium (ICM), trapped in their potential wells. Cosmic microwave background (CMB) photons passing through a massive cluster interact with the energetic ICM electrons with a probability of tau approx 0.01. This inverse-Compton scattering preferentially boosts the energy of a scattered CMB photon, causing a small (ltapprox 1 mK) distortion in the CMB spectrum, known as the Sunyaev-Zel'dovich effect (Sunyaev & Zel'dovich, 1972; Sunyaev & Zel'dovich, 1970). The SZE is proportional to the pressure integrated along the line of sight, DeltaT propto integ ne Te dell. X-ray emission from the ICM has a different dependence on the density SX propto integ ne2 LambdaeH dell, where LambdaeH is the X-ray cooling function. Taking advantage of the different density dependences and with some assumptions about the geometry of the cluster, the distance to the cluster may be determined. SZE and X-ray determined distances are independent of the extragalactic distance ladder and provide distances to high-redshift galaxy clusters. This method does not rely on clusters being standard candles or rulers and relies only on relatively simple properties of highly ionized plasma.

The promise of direct distances has been one of the primary motivations for SZE observations. Efforts over the first two decades after the SZE was first proposed in 1970 (Sunyaev & Zel'dovich, 1972; Sunyaev & Zel'dovich, 1970) yielded few reliable detections. Over the last decade, new detectors and observing techniques have allowed high-quality detections and images of the effect for more than 60 clusters with redshifts as high as one. SZE observations are routine enough to build up samples of clusters and place constraints on cosmological parameters.

The SZE offers a unique and powerful observational tool for cosmology. Distances to galaxy clusters yield a measurement of the Hubble constant, H0. With a sample of high-redshift clusters, SZE and X-ray distances can be used to determine the geometry of the Universe. In addition, the SZE has been used to measure gas fractions in galaxy clusters (e.g., Myers et al., 1997; Grego et al., 2001), which can be used to measure the matter density of the Universe, Omegam, assuming the composition of clusters represents a fair sample of the universal composition. Upcoming deep, large-scale SZE surveys will measure the evolution of the number density of galaxy clusters, which is critically dependent on the underlying cosmology. In principle, the equation of state of the "dark energy" may be determined from the evolution of the number density of clusters.

In this review, we first outline the properties of the SZE in Section 2 and provide a brief overview of the current state of the observations in Section 3. SZE/X-ray determined distances are discussed in Section 4, briefly discussing the current state of SZE/X-ray distances, sources of systematics, and future potential. SZE surveys are briefly discussed in Section 5 and a summary is given in Section 6. The physics of the SZE is covered in previous reviews (Sunyaev & Zel'dovich, 1980; Birkinshaw, 1999; Rephaeli, 1995), with Birkinshaw (1999) and Carlstrom et al. (2000) providing reviews of the observations. Carlstrom et al. (2002) provide a review with focus on cosmology from the SZE, with special attention to SZE surveys.

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