The Langlands functoriality conjecture is one of the basic problems in the theory of automorphic forms and representations. In the past four decades, there was essentially no progress made until a few years ago when the Langlands functoriality was established for generic cuspidal automorphic representations from classical groups to general linear groups in a series of papers by Cogdell$-$Kim$-$Piatetski$-$Shapiro$-$Shahidi, Ginzburg$-$Rallis$-$Soudry, and Jiang-Soudry. Many important applications were found afterwards. The problem of establishing the theory for general cuspidal automorphic representations remains a big open problem. In this talk, I will report on some recent progress on this problem, based on my work and my work with Soudry