Given a compact (Hausdorff) group G and a closed subgroup H of G, in this paper we present symbolic criteria for pseudo-differential operators on the compact homogeneous space G/H characterizing the Schatten-von Neumann classes Sr(L 2 (G/H)) for all 0 < r ≤ ∞. We go on to provide a symbolic characterization for r-nuclear, 0 < r ≤ 1, pseudo-differential operators on L p (G/H) with applications to adjoint, product and trace formulae. The criteria here are given in terms of matrix-valued symbols defined on noncommutative analogue of phase space G/H × G/H. Finally, we present an application of aforementioned results in the context of the heat kernels.