Galactic environment is thought to be one of the key factors in driving the cosmic quenching of star formation in galaxies. The Fornax cluster is a nearby intermediate-mass cluster that is more representative of the clusters found in the Universe compared to other nearby clusters such as Virgo and Coma. Fornax thus represents an ideal environment to understand the relative role of hydrodynamic and gravitational processes affecting galaxies in crowded environment.

In this context, I will discuss the results of the Fornax3D magnitude-limited survey of galaxies in the Fornax cluster with MUSE integral-field spectral. Additionally, I will present the results of ancillary studies based on deep optical and radio observations (with VST and MeerKAT) revealing objects currently on-going star-formation quenching. To further gain insight on the physical mechanisms behind such phenomena, we derive the star-formation history of Fornax galaxies with a spectrophotometric approach to both MUSE integral-field spectroscopic and S-PLUS imagining data. At the same time we also explore Fornax-like clusters in the TNG-50 simulations to derive the neutral-gas predicted distribution both across the whole cluster and around individual galaxies, following this also in time. This gives us a view of both on-going gravitational and hydrodynamical interactions in the Fornax cluster galaxies as well as a gauge on the past impact that these had in driving their star-formation histories, which we can compare to model predictions.