It has long been known that the colorful variety of galaxies we see in the Universe is shaped by a combination of internal processes (e.g. feedback) and the environment in which galaxies live. In massive clusters, galaxies undergo strong environmental processes, leading to the suppression of their star formation activity. One of these mechanisms, perhaps the dominant one in galaxy clusters, is the ram pressure stripping (RPS) of the cold ISM, as galaxies travel at high velocity in the dense intracluster medium. Narrow band imaging surveys targeting the emission from ionized hydrogen have detected several tens of RPS tails. Until a decade ago, however, the properties of the stripped gas remained elusive, as the faint extended emission of the RPS tails required significant time investments to obtain follow-up optical spectroscopy. The MUSE instrument provided a breakthrough in this field, with its large FoV and unparalleled sensitivity. Observations of RPS tails became a routine. I will present our journey in resolving the physics of RPS, from the first observations of ESO137–001 in the Norma Cluster, revealing the surprising dominance of shocks and turbulence in the ionization of the tail. I will continue with the results from a statistical sample of a pure and nearly complete RPS sample, and on the reconstruction of the star formation quenching timescales. I will conclude by discussing the perspectives to extend these studies to high-z with future facilities.