Weyl law describes the asymptotic behavior of eigenvalues. We study the eigenvalue problem of the Schrodinger operators with singular potentials on compact Riemannian manifolds. In recent works with Xiaoqi Huang (University of Maryland), we proved the pointwise Weyl laws for the Schrodinger operators with critically singular potentials, and showed that they are sharp by constructing explicit examples on flat tori. This work extends the 3d results of R.L. Frank (Caltech) and J. Sabin (University of Paris-Saclay) to any dimensions, by a different method.