In this talk, we will discuss the theory of automorphic descents of Bessel-Fourier coefficients of classical groups of Hermitian type and its relation to the automorphic version of the branching problem and the reciprocal branching problem. In particular, we apply the theory of automorphic descents to study certain cases of generalized Gan-Gross-Prasad conjecture on the non-tempered case. This is joint work with Dihua Jiang.