The Sunyaev-Zel’dovich (SZ) effect is an important observational signature of galaxy clusters, the largest objects in the Universe today. In particular, the pairwise kinematic SZ signal probes the matter-velocity correlation function, scaled by the average optical depth of galaxy clusters, and is thus an interesting probe both from a cosmological and astrophysical point of view. In this talk, I will give an overview about our current cosmological understanding, highlighting the role of the SZ effect. I will present the current landscape of kinematic SZ measurements, including a recent measurement by the South Pole Telescope collaboration and the Dark Energy Survey collaboration, as well as insights from new, state-of-the-art simulations, and recent progress in the modeling of gas profiles of galaxy clusters.