This paper is a survey on explicit formulas for the Hilbert symbol on Lubin-Tate formal groups due to I.B.Fesenko, S.V.Vostokov and A.Wiles. I also give applications of Kummer''s formula to Von Staudt congruence, Kummer''s lemma, and Ankeny-Artin-Chowla congruence.
