Relatively supercuspidal (RSC) representations are the analogue object of supercuspidal representations in the relative Langlands program. In this talk, using top degree Ext-groups via the Schneider-Stuhler duality, we consider the classification of RSC representations in terms of cuspidal supports and in terms of Arthur parameters for the associated spherical varieties. Especially, we shall focus on the Gan-Gross-Prasad case and the Flicker-Rallis case. Joint work with Yangyu Fan.