  This paper intends to give a brief survey of the developments on realization
of surfaces into $ R^3$ in the last decade. As far as the local isometric
embedding is concerned, some results related to the Schlaffli-Yau conjecture
are reviewed. As for the realization of surfaces in the large, some
developments on Weyl problem for positive curvature and an existence result for
realization of complete negatively curved surfaces into $ R^3$, closely related
to Hilbert-Efimov theorem, are mentioned. Besides, a few results for two kind
of boundary value problems for realization of positive disks into $R^3$ are
introduced.
