In this talk we will discuss symplectic embeddings of ellipsoids into arbitrary symplectic manifolds. We will establish that sufficiently thin ellipsoids enjoy symplectic flexibility, that is, they can be embedded into a target symplectic manifold with a rational cohomology class as long as the volume requirements are met. As a consequence we will generalize to all dimensions Biran's four-dimensional result on symplectic packing stability, which result states that for all numbers k suficiently large one can always get a volume filling symplectic k -embedding into a given symplectic manifold with rational cohomology class. This is joint work with Richard Hind. In the second part of the talk, if time allows, we will discuss an ongoing collaboration with Richard Hind and Emmanuel Opshtein aiming to establish the packing stability conjecture for symplectic four manifolds with irrational cohomology classes