Abstract: The large-scale velocity field of matter is a sensitive probe in several exciting areas of cosmology and astrophysics, including cosmological parameters, dark matter halo models, and electron profiles. In addition, by combining it with the large-scale velocity and galaxy overdensity fields, one can obtain competitive constraints on local primordial non-Gaussianity. In this talk, I will introduce kinematic Sunyaev–Zeldovich (kSZ) tomography, a modern technique for reconstructing the large-scale velocity field, followed by a novel development in an optimal power-spectrum estimator that outperforms conventional approaches with highly compressed computation time. I will present its latest application to observations from the Atacama Cosmology Telescope and DESI-LS (Legacy Survey), yielding a ~12σ detection of the kSZ signal—an improvement factor of ~3 compared to earlier studies. With upcoming data from the Simons Observatory and the Vera C. Rubin Observatory, there is a promising outlook for kSZ velocity reconstruction.