Endoscopy structures of automorphic forms was one of the
basic structures discovered through the Arthur-Selberg trace formula method to establish the Langlands functoriality for classical groups.

In this talk, we will discuss my recent work on characterization of the endoscopy structure in terms of the order of pole at s=1 of certain L-functions, and in terms of a family of periods of automorphic forms, which was discovered jointly with David Ginzburg. At the end, I may discuss how to contruct the
endoscopy transfer by integral operators, which is
a joint work with Ginzburg and Soudry.