Abstract: The bimodal distribution of galaxies on the M_*-SFR plane implies a rapid transition from the state of star-forming to quiescence, which process is usually referred to as galaxy quenching. Previous studies have established that galaxy quenching is regulated by both internal and external processes. The internal quenching process is also known as mass quenching since it is primarily dependent on stellar mass, and a variety of physical mechanisms have been proposed to explain this phenomenon. One way to break the degeneracy among these models and obtain deep insight into the underlying physics is to explore its relation to secondary quantities other than stellar mass. In this talk, I will present our recent effort along this line by investigating how the quenching of central galaxies depends on their large-scale environment and the assembly history of their host halos.