Strange duality is a conjecture formulated in 1990s, which asserts a duality between the global section spaces of determinant line bundles over two moduli spaces of semistable sheaves over a smooth projective scheme X. When X is a curve, this conjecture has been proved around 2007. When X is a surface, there is so far no general set-up for this conjecture; but under some assumption the conjecture can be extended. There is not much known for surfaces on the conjecture. In this talk, I will first introduce the formulation of the conjecture, then survey shortly the proof for curves , and finally mention some progress for surfaces, especially my result for rational surfaces and my strategy as well.