  In his Ph.D. thesis, John Tate attached the (abelian) local constants to the
characters of a non-Archimedean local field of characteristic zero. Robert
Langlands proved the existence theorem of a non-abelian local constant of a
higher-dimensional complex local Galois representation. In 1990, Helmut Koch
summarized Langlands' strategy for the existence of a non-abelian local
constant (group theoretically). The Brauer induction formula plays a crucial
role in Langlands' proof. Robert Boltje gives a canonical version of the Brauer
induction formula. In this paper, we review Langlands' strategy using Boltje's
canonical Brauer induction formula. We then review various properties of local
constants, some applications, and open problems.
