  Functoriality conjecture is one of the central subjects of the present-day
mathematics. Functoriality is the profound problem formulated by Robert
Langlands in the late 1960s in order to establish nonabelian class field
theory. In this expository paper, we describe the Langlands-Shahidi method, the
local and global Langlands conjectures and the converse theorems which are
powerful tools for the establishment of functoriality of some important cases,
and survey the interesting results related to functoriality conjecture.
