In this paper, we study the problem of restricting a square integrable representation of a connected semisimple Lie group to a reductive subgroup. Using a geometric method of restricting sections of a vector bundle to a submanifold, we obtain information about both the discrete and the continuous spectrum. We also show the (L²,L²)-continuity of the associated Berezin transform and that, under suitable general conditions, the Berezin transform is (L²,L²)-continuous for 1≤p≤∞