The endoscopy structure of automorphic forms was discovered by Langlands in early 1980's, and has been recently established by Arthur and also by Mok for quasiplit classical groups, based on the fundamental work of Bgo, Waldspurger, Moeglin, Laumon, Chaudouard, and others, via the trace formula method. In this talk, we will explain our work on explicit construction of endoscopy correspondences via automorphic integral transform, based on the idea of classical invariant theory, in particular that of Howe duality.