The cosmic star formation rate density has been declining since z~2-3, suggestingthat the cessation of star formation has been the dominating process in galaxyevolution since then. However, it is unclear how the star formation gets quenchedinside the galaxies and what physical mechanisms have been driving this process.Current integral field unit (IFU) surveys such as CALIFA and MaNGA areproviding resolved spectroscopy for large samples of galaxies in the local Universe,allowing the star formation histories across the whole galaxy area to be studiedwith high accuracy. In addition, maps of molecular gas are also being obtained byarrays of radio antenna, thus providing additional data for linking the star formationand gas accretion processes in the IFU era. I'll briefly review previous studies on thesingle-fiber SDSS spectroscopy, and present our recent work based on the CALIFA,MaNGA and CARMA-EDGE surveys, particularly focusing on the roles ofenvironmental effect, dark matter halo, and internal structure and nuclear activity indriving galaxy evolution.