Abstract: Since Whitney's classical result of smooth embedding of manifolds into $\mathbb R^n$, one of the themes in geometry has been the existence of embeddings that preserve additional structure, for example, isometric embeddings of Riemannian manifolds or embeddings as symplectic or isotropic submanifolds into euclidean spaces with the standard Riemannian or symplectic structure. In this talk I will discuss some old and new problems concerning embeddings with special properties of complex or real manifolds into complex Euclidean spaces. We start with Stein manifolds and then discuss totally real embeddings and embeddings with special approximation properties. These problems have a topological component, such as Gromov's h-principle and Morse theory.