Outflows fundamentally alter the chemical composition, structure, and star-formation activity of galaxies, and are therefore one of the most important processes shaping galaxy evolution. However, our understanding of outflow physics is still in its infancy, and the role of outflows in quenching star-formation is a topic of ongoing debate. In this talk, I will highlight recent observational breakthroughs enabled by the James Webb Space Telescope (JWST), the Very Large Telescope (VLT) and the Atacama Large Millimeter Array (ALMA). Specifically, I will examine the role of AGN-driven outflows in quenching massive galaxies at cosmic noon, and compare the mechanisms accelerating star-formation driven outflows at different redshifts. Outflows are just one component of the cosmic baryon cycle, and I will conclude by discussing how future observations with VLT/MAVIS, 30m-class telescopes and the Square Kilometer Array which will enable us, for the first time, to connect the dots between inflows, outflows and star-formation over much of the history of the Universe.