  Nambu proposed an extension of dynamical system through the introduction of a
new bracket (Nambu bracket) in 1973. This article is a short review of the
developments after his paper. Some emphasis are put on a viewpoint that the
Nambu bracket naturally describes extended objects which appear in M-theory and
the fluid dynamics. The latter part of the paper is devoted to a review of the
studies on the Nambu bracket (Lie 3-algebra) in Bagger-Lambert-Gustavsson
theory of multiple M2-branes. This paper is a contribution to the proceedings
of Nambu memorial symposium (Osaka City University, September 29, 2015).
