My talk will focus on the development and applications of the “filtration method”, which was introduced by Faltings and Wustholz in 1994 and developed by Evertse and Ferretti, and independently by Corvaja-Zannier. Further works were done by Levin, Autissier, and by Vojta and myself. In particular, I will present the recent work about a general arithmetic inequality, as an extension of the Schmidt's subspace theorem, established by Vojta and myself, as well as its applications. If time permits, I'll also describe its relationship with the algebro-geometric notion of the stability concerning the existence of Kahler-Einstein metric on Fano varieties.