The Sunyaev-Zel’dovich (SZ) effect is an important observational signature of galaxy clusters, the most massive gravitationally collapsed objects in the Universe today. In particular, the pairwise kinematic SZ signal probes the relative motion of these objects, scaled by their integrated electron density, 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 and the formation of structure in the Universe, highlighting the role of the SZ effect. I will present the current landscape of kinematic SZ measurements, as well as insights from new, state-of-the-art simulations, and recent progress in the semi-analytic modeling of the gas inside galaxy clusters, which sources the SZ signal. I will conclude with some promising applications of Machine Learning in the domains Cosmology and Astronomy.