One of the key open questions in galaxy evolution today is how and why galaxies (almost) cease to form stars towards the end of their life cycle. The so-called quenching of star formation has been shown to be driven by a combination of reduced molecular gas fractions and low star-forming efficiencies. However, the detailed physical processes behind regulating these quantities, as well as the associated timescales, remain an active area of research. I will present new insights into galaxy quenching and the drivers of star formation fluctuations from various angles: Using the first data release of the MaNGA-ARO Survey of CO Targets (MASCOT; Wylezalek et al. 2022), I will investigate the more imminent impact of feedback processes onto molecular gas properties at low redshift in conjunction with ionised gas kinematics and the gas-phase metallicity distribution. Specifically, I will focus on weak outflows within the subset of active galaxies below the Main Sequence. Complementary, I will also report on the JWST Early Release Science program Q3D, which will zoom into strong outflows within luminous quasars at different redshifts (0.4 < z < 3). Finally, I will address to what extent the present-day star formation in galaxies may be traced back to their early histories of star formation on Hubble timescales. For this purpose, I will reconstruct the star formation histories of massive star-forming SDSS-IV MaNGA galaxies (z~0.04) via full spectro-photometric fitting with the novel stellar population synthesis code Bagpipes (Carnall et al., 2018).