The cosmic star formation rate density has been declining since z~2-3, suggesting that the cessation of star formation has been the dominating process in galaxy evolution since then. However, it is unclear how the star formation gets quenched inside the galaxies and what physical mechanisms drive this process. Current integral field unit (IFU) surveys such as CALIFA and MaNGA are providing resolved spectroscopy for large samples of galaxies, while CO intensity mapping such as the EDGE survey is providing spatially resolved molecular gas mass density. These data allow the star formation histories and cold gas distribution across the whole galaxy area, and thus the quenching processes to be studied with high accuracy. I will talk about our recent works based on these surveys, particularly the roles of internal structure (e.g. bars),molecular gas and environmental effect in driving the star formation quenching processes.