The classical Weyl problem asks isometric embedding of positively curved compact surface in to R^3, which was solved by Nirenberg in 1950s. Pogorelov subsequently solved the Weyl problem in hyperbolic space H^3, he also considered the problem in general 3D Riemannian manifolds. Solutions to Weyl's problem in R^3 and H^3 have important applications in general relativity, e.g. the Brown-York, Liu-Yau and Wang-Yau quasi local masses. We report some recent progress on the Weyl problem of isometric embeddings of (S^2, g) to general 3D ambient space: the openness and non-rigidity results C. Li and Z. Wang, the curvature estimates for immersed surfaces jointly with Siyuan Lu, and the existence of solutions of the problem when the surface contains no horizon. We will also discuss the problem when horizon arises.