We will talk about a singular Donaldson-Uhlenbeck-Yau theorem for stable reflexive sheaves over projective normal varieties smooth in codimension two. This improves known results regarding normalized tautological classes. Then we will study both the algebraic and analytic degenerations of semi-stable bundles/Hermitian-Yang-Mills connections by allowing the base manifolds to form normal singularities. As an application, we will explain how this result is related to the Mehta-Ramanathan restriction theorem. The talk is based on joint work with Richard Wentworth.