Galaxy clusters have been observed mainly in the optical and X-ray regions, and played an important role in probing the universe in addition to the cosmic microwave background (CMB) and the three-dimensional distribution of galaxies. In recent years, another method of observing galaxy clusters in mm and sub-mm bands, the Sunyaev-Zel'dovich (SZ) effect, has made significant progress. This is based on the inverse Compton scattering off the CMB photons due to the high-temperature intracluster gas, which was proposed in early 1970's. This method has a remarkable advantage that the observed flux is independent of the distance to the cluster. Recent significant progress in detectors promises that the SZ effect will indeed lead the cluster observation in this decade. This article presents a summary of the past and the present researches in the SZ effect and discusses the future prospects, with particular emphasis on theoretical and observational achievements in Japan.