The purpose of this paper is fourfold. First, we show that the Langlands' functorial lift of a generic cuspidal representation of SO 2n + 1 to GL 2n is of the form Ind σ1⊗…⊗σk, where σ i 's are (unitary) cuspidal representations of GL2ni such that L(s,σi,Λ2) has a pole at s=1, strengthening the recent result of Cogdell, Kim, Piatetski-Shapiro, and Shahidi. It uses the result of Barbasch and Moy on the spherical unitary dual,and the result of Ginzburg, Rallis, and Soudry that says that ifL(s,σ×t), where σ is a cuspidal representation of GLm and t is a generic cuspidal representation of SO2n+1, has a pole at s=1, then L(s,σ,Λ2) has a pole at s=1. Second, we give an application of the above result to the problem of determining the residual spectrum of SO2n+1 coming from maximal parabolic subgroups,with the assumption that the completed symmetric square L-function of GLn is holomorphic except possibly at s=0,1. Third, we describe the residual spectrum of SO5 and GSp4, defined over a number field. Even though Sp4 and SO5 are closely related (isogenous), their residual spectrums are quite different. Fourth, we give a conjectural description of the residual spectrum of SO2n+1 coming from arbitrary parabolic subgroups, assuming some standard global and local conjectures.