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 have been driving this process. Current integral field unit (IFU) surveys such as CALIFA and MaNGA are providing resolved spectroscopy for large samples of galaxies in the local Universe, allowing the star formation histories across the whole galaxy area to be studied with high accuracy. In addition, maps of molecular gas are also being obtained by arrays of radio antenna, thus providing additional data for linking the star formation and gas accretion processes in the IFU era. I'll briefly review previous studies on the single-fiber SDSS spectroscopy, and present our recent work based on the CALIFA, MaNGA and CARMA-EDGE surveys, particularly focusing on the roles of environmental effect, dark matter halo, and internal structure and nuclear activity in driving galaxy evolution.