The Sunyaev-Zel’dovich effect (SZE) is a relevant probe for cosmology and astrophysics. A multi-frequency approach to study the SZE in cosmic structures turns out to be crucial in the use of this probe for astrophysics and cosmology. Astrophysical and cosmological applications to galaxy clusters, galaxies, radiogalaxies and large-scale structures are discussed. Future directions for the study of the SZE and its polarization are finally outlined.